Paired Voting System PVS

1 Introduction

Decisions are often made by within a group of people who do not completely agree. Rather than one person imposing their will on others, most people recognize that in most cases the majority is best suited to make decisions that affect the group or society.

Paired voting system (PVS) takes care of the Condorcet^[2] winner Criterion problem which is outlined in the excellent Wikipedia article. . PVS takes care of this problem by not insisting the top ranked Choice is the winner in all pairings. Paired Voting System (PVS) is transparent and easy to understand. Every choice is paired with every other choice for each voter and important values are determined from each pairing. These are WINS, TIES, FORS, FIRSTS These are analyzed final rankings calculated.

In brief CHOICES are ranked by the number of WINS the each achieve is a paired comparison with every other voter. Other parameters are brought in to resolve TIES in the number of WINS achieved.

Paired Proportional Weighed Voting System (PPWVS) extends PVS to include 2nd place standings, in the form of proportionality to influence voting in the legislature, An exceptionally good outcome.

2 Mathematical summary:

∫_(v=0)^(v=n)▒〖PVS(C₁r₁,〗 C₂r₂…Cₘrₘ) ⇶ (C1R1, C2R2…CmRm)

v= voter, n =number of voters C = Choice, m = number of voices r = a preference ranking provided by a voter (RNK) R= A choices Rank after PVS has performed the calculation

2.1 Purpose of the Paired Voting System

is to serve as the best alternative when ranking choices. An extremely poor way of making choices is the First Past the Post System (FPTP/SVS). The use of this system is slowly degrading democracy and can easily be seen if one looks at the USA and what is happening there. You end up with control of the government by minorities

20230524 When considering choices some of the goals are to:

Ensure majorities (not minorities) make the final choices and exercise control.
Provide for a path to Proportional Representation.
Increase voter engagement.
Provide for clearer choices.
Provide an order for the choices from top to bottom.

Democracy worldwide suffers under FPTP/SVS. When minorities are given control because of FPTP/SVS you end up with the wrong parties elected, the wrong leaders, the wrong candidates and the wrong decisions.

2.4 Implementation PVS is the most effective and obvious way to manage and create choice data which when analyzed will generate the best choices. The resultant data could then be utilized to work out the kinks in proportionality. It cannot be emphasized enough that the implementation of Proportionality must be carefully done, or a non-functional government could result. If changes are to be made from other systems, it would be strongly recommended to stage the implementation so that PVS is implemented first followed by Proportionality.

3.0 Comparisons

3.1 1st Past The Post:^[3]

First past the Post: A terrible system where voters can only cast ONE Vote. In that type of system all other voter intentions are ignored and invariably this leads to decisions made that are supported only by Minorities. Suppose you had five candidates representing five parties running for office – ISIS with a 19% following, Al Qaeda with a 20% following, Fascists with a following of 21%, a Communists party with 22% and a centrist party with a following of 18%. I call this a split vote system or SVS.

3.2 Instant Runoff (IRV):^[4]

In the following example I will show how the instant Run Off system fails, Using the PVS the Centrist party WIS against all other candidates on one-on-one pairings and emerges the Winner. Under IRV the centrist party is culled in the first step. As will become evident this is a mistake. The Communist Party was victorious with only 3 WINS. The Communist would have lost against the centrist Party. Instant run off systems lead to minority results Suppose you had five candidates representing five parties running for office – ISIS with a 19% following, Al Qaeda with a 20% following, Fascists with a following of 21%, a Communists party with 22% and a centrist party with a following of 18%. In the First past the Post systems Centrists would lose, and this means a minority government. In an instant runoff system, the Centrist Party would be culled in the first round and depending on the splits after it would be a tossup between the Fascist and the Communists. Example: After a long and Tedious process Communist Party will emerge as the victor. Step one: Only 1st place votes are considered and the party with the least 1st place votes is cut out. The centrist party will be cut out of the voting.

Step two:

Remaining 1st place votes are considered and the party with the least 1st place votes is cut out. Votes are reallocated in accordance with preference.

Step three:

The remaining 1st place votes are considered and the party with the least remaining 1st place votes is cut out. Votes are reallocated in accordance with preference. The Fascist Party will be removed.

Step Four:

The remaining 1st place votes are considered and the party with the least remaining 1st place votes is cut out. The Communist Party emerges Victorious with 62% of the remaining first Place votes.

3.3 Condorcet Method ^[5]

If the analysis of the example Presidential election the results would be inconclusive as the choice ratios between the 1st place and second place candidates are the same. In a Condorcet election the Winner is the candidate who beats out all other candidates in a one on one pairing and this is what the choice ratios measure.

Example: In the other example election the Condorcet System would produce a WIN by the Centrist party.

3.4 Paired Voting System:

With Paired Voting System PVS. WHY - because all votes count. PVS is designed to replace all other forms of decision making, and can be applied to shareholder votes, director elections, candidate selections, competitions, choices at management meetings and anywhere where multiple choices must be made. Voters state their preferences in RNK order from their top Choice to their last Choice. Each pairing of Choices results in a FOR which applies to one of the Choices, depending on which numerical RNK value was assigned by the voter. If the voter sets the numerical values of each Choice to be the same the FOR is split and each Choice is assigned ½ FOR. For Each Voter-The sum of the FORS for each Choice pairing is compared. The winning Choice in a pairing is the choice who receives the most FORS. The Choice receives 1 WIN if he beats out all other Choices in that pairing. If there are 4 Choices under consideration a Choice can obtain a maximum of 3 WINS. The Winning Choice among all the Choices is that Choice which has the most WINS. If the WINS are tied then a comparison of TIES is made and if that comparison results in a tie, then the winner is the Choice that receives the most overall FORS. If that still results in a tie, then the individual FORS each Choice are compared. The top ranked Choice is clearly supported by a majority in this way and each final vote pairing captures 100 percent of votes in play between the top two choices. Because of the way PVS (Paired Voting System) works it allows for a ranking of all choices. The system therefore provides for the case where voters can be given a list of choices including a “not acceptable choice a so called WDC (will not do choice).” In many cases voters are provided with Choices none of which are acceptable and if no Choices are ranked above WDC this would require a re-election. Since PVS fairly represents all voters and choices, it would be possible to add other choices to the ballot without compromise. Sometimes the decisions made as to which names are placed on the ballot in the first place can be overly political and so in the USA to avoid this problem, Ron Desantis and Donald Trump could both be placed on the Presidential ballot without compromising anyone’s base. Naturally, Trump’s base would choose Donald Trump as No 1 and Ron Desantis as number two. On the other hand, the democrats would also field two names and so both sides would preserve their respective bases without compromising their voters or their chances. Al voters and sides have a strong voice in the outcome as their RNKs could be applied to and influence both sides as well as all candidates. This would compel all candidates to represent all voters. Although a voters first choice might not win, they would have a say in who on the other side will end up being President. In the example provided there are only 4 voters and so the race becomes very close.

Presidential Example:

Joe Biden Wins as he has the greatest number of WINS at 1.

Centrist Example

Centrist Example …. PVS establishes the greatest number of WINS for the Centrist party. Interestingly, when the minority voters vote their preferences their number 2 choice is the centrist party. This clearly shows that from a uniting point of view the Centrist party has the best chance of bridging divides and fostering unity.

4 Definitions

4.1 Choices

A Choice represents a selection from a variety of other choices. Examples:

Courses of action
Board members
Elected representatives.
A, B, or C
Committee members.
Budget amounts

== 4.2 Choice Ratio. The Choice Ratio for each choice is the percentage of winning (FORS) that occurs because of their individual pairings with the next highest ranked candidate.

In the example shown below the Conservatives have 6985 FOR votes against the Liberals and the Liberals have 35,101 FOR votes against the Conservatives. In resolving the choice ratios for this pair, the Conservatives have 16.60% of the FORS.

It is possible for a 2nd ranked candidate to have a higher choice ratio than the 1st ranked Candidate. This would be an extremely rare event and would be an example of a complication in the Condorcet voting system. [[1]]

PVS avoids dealing with the Condorcet complication simply by the manner in which it performs its calculations. Here is an example from a small number of voters to make the point.

When the data is analyzed, PVS provides the following results as a first stage. Note that Donald has registered 3 FORS in a pairing with Danny and conversely Danny has registered 2 FORS in his pairing with Donald. The Choice factor for A then becomes 40% and for B becomes 60%. This means that in a one-on-one pairing between Danny and Donald, Donald would rank ahead. This is a key point as a calculation done this way reveals a hidden truth that an SVS system would never reveal. The final determination is made in order of WINS, TIES, Total FORS, 1st Place RNKS. Although Donald can win over Danny in a one-on-one pairing, he would lose against Joe using the full power of PVS. The main reason to establish Ranks without emphasizing choice ratios is to avoid closed circles where no one is a winner because they all lose to someone on a direct pairing.

4.3 Elevations and Demotions

4.3.1 Minimum Choice Ratio (MCR):

A candidate may be elevated if his choice ratio is above the minimum. This refers to changes in the elected status of a candidate from either “Non-Elected” to “Elected” which is an elevation or from “Elected” to “Non-Elected” which is a demotion. Where PVS data is used to generate an elevation or demotion of candidates, then one can stipulate how choice ratios will be analyzed in the context of the global election in order to achieve this. For example a rule could be set to ensure that only candidates with a Choice Ratio of at least .45 may be elevated and that Candidates with a Choice Ratio of over .55 may not be demoted. This will be discussed further in the Proportional representation section. In the example below. To balance out the candidates to match the needs of proportional representation the Conservative Candidate could be elevated to elected and the Liberal Candidate could be demoted to not elected.

4.4 First Place Votes in PVS

PVS tracks First Place RNKS in PVS. There is a special case where a voter has ranked multiple choices with a RNK of 1. In that case the count of First places RNKs is shared among all the 1st place choices. EG if choice A holds a RNK of 1 and so does choice B then each Choice will be assigned 1 First place vote count of ½. Example:

4.5 FOR: Vote Counts

When a RNK set by a voter favors one choice over another then the favored choice is assigned a “FOR.” The size of the numerical separation between the two RNKs is not considered as any rule that attempts to resolve the separation issue would certainly be too complex to be useful. One is simply larger than the other Consider the following paired Preferences. All the examples show Choice A is the first RNK and Choice B is the second RNK. EG: A, B: 1,2 Voter shows support for Choice A in this pairing given that Choice A is RNKED ahead of B. Choice A FOR= 1, Choice A “1st place vote”= 1

A,B:2,7 Voter shows support for Choice A in this pairing given that Choice A is RNKED ahead of B. Choice A FOR= 1

A:B: 1,0: Choice A FOR= 1, Choice A “1st place vote”= 1

A:B: 2,2: Choice A FOR= 1/2 , Choice B FOR= 1/2

A:B: 1,1: Choice A FOR= 1/2 , Choice B FOR= 1/2 Choice A “1st place vote”= 1/2 , Choice B “1st place vote” 1/2 Example:

4.5.1 Example "FORS" from pairings

Computer calculates “FORS” based on the RNKs provided by the voters. For example, if we analyse the results from a single voter and five candidates, the candidates are RNKed 1st, 2nd, 3rd,4th, and 5th.

Each party has accumulated “FORS” from successful pairings. You will notice the Green party for this ONE voter has zero “FORS.” However, the Green party will accumulate ”FORS” from other RNKs set up by other voters.

4.5.2 FORS detailed examples

There is more detail on how this works in a subsequent section of the paper. Let us say there are 10 RNKS cast for Candidate A and Candidate B. 3 RNKS are in favor of candidate A and 3 RNKS are in favor of Candidate B.(6 RNKs) 1 RNK is a tie with both A and B, given a RNK of 0 (1 RNK) 3 RNKS are non-zero but equal. (3 RNKs) Calculated FORS Including ties of equal value. The total FORS for A are 3+3*.5 =4.5 The total FORS for B are 3+3*.5=4.5 The result is a tie. Choice Ratio for both is .5.

Now change the mix so that A gets 4 FORS and B gets 2 FORS (6) The results then look like this. Calculated FORS Including ties of equal value. A 4+3*.5= 5.5 B 2+ 3*.5= 3.5 Choice Ratio for A is 5.5/9=.61 Choice Ratio for B is 3.5/9=.38

4.6 Lost Votes

The narrow view of what this means is that if a voter’s intentions at the ballot box have no influence on the outcome, then the vote is a lost vote. In the first past the post system any vote is cast for any other candidates other than for the first or second place candidates are considered lost as other votes have no influence on the elected candidate.

4.7 Pairings

4.7.1 Choice Pairing

Each choice paired with each other choice establishes data for further analysis.

4.7.2 Final Pairing

PVS provides a rank for each candidate. The Final Pairing refers to the candidate pair of a candidate and the highest other candidate in the rankings. If you have 4 candidates ABCD ranked 1,2,3.4. The Final Pairings set up the Choice Ratios.

Choice ratio AB = (FORS AB)/ (FORS AB +FORS BA)
Choice ratio BA= (FORS BA)/ (FORS AB +FORS BA)
Choice ratio CA= (FORS CA)/ (FORS AC +FORS CA)
Choice ratio DA= (FORS DA)/ (FORS AD+FORS DA)

4.7.3 Top Pairing

PVS will calculate a rank for each candidate. The top pair is the candidate pair whose ranks are 1 and 2.

4.8 Proportional Representation

Characterizes electoral systems by which divisions in an electorate are reflected proportionately in the elected body either by weighing of the votes or by adjustments in elected numbers for the various divisions. The example discussed here is modelled on the Canadian Federal Election of 2015

4.8.1 Proportionality uplifts using Choice Ratios of the first and second place candidates.

Representation is direct in the case of first place and second-place candidates through a proportional uplift. This is a vast improvement to FPTP/SVS, and an improvement to simple PVS. A restriction of the proportionality criteria to the first and second-place choices reduces the impact and confusion caused by having multiple candidates who have not reached the first or second position, and whose results are thrown into the mix, especially when ridings are composed of various numbers of candidates in various size ridings. In summary the proportional calculations move the Choice Ratios from the first and second place candidates only, into the respective parties.

4.9 PPWVS Paired Proportional Weighed Voting System

Paired choices from PVS are used to set up Choice ratios. Proportional uplifts to the legislature flow from Choice Ratios The sum of the choice ratios for the top-rated pair in each riding always totals 1. Weights are used to achieve proportional representation.

4.10 PPVS Paired Proportional Voting System

Demotions and elevations of candidates achieve Proportional Representation.

PPWVS is the precursor to PPVS as once the demotions and elevations kick in the weight assigned to votes at the legislature can be eliminated or reduced.

4.11 Rank

The term Rank refers to the order of the final choices as output from a PVS analysis. Rank is differentiated from the term RNK which is how the voters see the order of the choices. You can think of this as Final Selection Rank as opposed to RNK (Voter Rank) which is the voter input at the ballot box. PVS Rank order is determined by the following steps when comparing choices. WINS- take precedence. If WINS are inconclusive, PVS compares TIES PVS Compares Total FORS- based on all pairings when prior comparisons are inconclusive. PVS Compares 1st Place RNKS when prior comparisons are inconclusive. This sequence plays out in the example below. The actual RNKS of the voters are shown here for clarity. In the example shown there were 10 voters and 10 choices. After a Randomined vote was set up the following results were obtained.

These are from the detailed PVS data produced from the RNKs above.

Choices 4 and 7 were tied in almost all items with the tie breaker being in the number of first place RNKS. Note that Choice 8 was ranked 1st and had only one 1st place RNK. In an FPTP/SVS voting system Choice 8 would not have had a chance and there would have been a 3 way tie for 1st place Rank, being (choices A,9,4)

4.12 RNK

When a voter RNKS his choices he does so by indicating his preferences in order from Best (1) to Last (N). A RNK of 0 indicates a voter does not wish to indicate a preference for that choice. We call Preferences RNKs for short. A voters’ first preference of candidate would be RNK 1, followed by RNK 2 and so on. For each choice, the voter sets out a number that shows the computer what voter RNKs are with respect to other choices. Choices can be RNK’s the same by a voter.

Voter 1 selection could look like this.

RNK Definitions to show TIE values being ascribed to separate candidates

Voter 1 could have also made his selection like this

RNK Definitions illustrating a RNK of 0 being set for a Candidate

4.13 RNK1234

The usual order of RNK’s is from the best (lowest RNK) to the worst(highest RNK). In some cases such as events in competitions the order is reversed from the best(highest RNK to the worst (Lowest RNK). For example if high jump results are entered the highest RNK( Jump) would have to be the best.

4.14 WDC or FAIL Alternative

The WDC, FAIL concept is a relatively unknown and little used concept in today’s voting world. To completely represent the wishes of each voter a WON’T DO CHOIVE (WDC) choice needs to be considered. This can easily and without fanfare be accommodated using PVS. In the case of a simple YES-NO vote on say a motion, the WDC choice is equivalent to the NO choice or a failure to meet minimum standards. In the case of electing a leader from a list of candidates the WDC choice if selected ahead of all the candidates would mean that none of the candidates are acceptable. The message is clear, if a candidate(s) has not met the WDC threshold he is not acceptable and another candidate from outside of the current slate of candidates must be considered and added to the slate of candidates. Suppose there were three board members to be elected and PVS returned a slate of directors ranked as follows:

WDC
Candidate A
Candidate B
Candidate C

then none of the candidates would be acceptable and the shareholders would have to go back to the drawing board to select additional candidates for consideration and hold a revote If on the other hand the returned slate was as follows

Candidate A
WDC
Candidate B
Candidate C

Then candidate A would be acceptable to the shareholders. Candidates B and C would not be acceptable since they rank below the WDC choice. Concept is important when the wishes and preferences of the voters are to be provided for and considered.

4.15 Minimum Choice Ratio

Computer proportionality calculations establish which candidates might be elected by elevation. This means other candidates might be demoted. A Minimum Choice Ratio is set to enable an elevation. For example: A Minimum Choice Ratio of .45 would mean that anyone who has a choice ratio of under .45 cannot be elevated and anyone who has a choice ratio of over .55 cannot be demoted since a .55 demotion corresponds to a .45 elevation. IE 0.45+0.55 = 1.

4.16 VUUP Voter Units of Political Power

This concept serves to answer a big question. How much power do voters have? Suppose we have a FPTP/SVS result where the winner has 25% or the 1st place votes. This means that on average a voter carries a weight of only 25% at the polls. VUPP=.25 Suppose we have a FPTP/SVS result where the winner has75% of the 1st place votes. This means that on average a voter carries a weight of 75% at the polls. VUPP = .75 I discuss this more elsewhere in this paper to illustrate how VUPPs vastly increase with PVS and Proportionality. RNKing candidates allows voters to exercise better control over their VUPPs.

In the example provided, the voter has shown some support for 4 candidates. The last candidate has not received any support from this voter no matter what the Top Pairing is.

There are other options whereby the voter can withdraw support from candidates.

5 PVS Paired Voting System

Every Vote matters. PVS output ranks choices from top to bottom. PVS provides majority support for an elected candidate. The minority associated with the second Ranked Candidate is not directly considered but by the virtue of PVS, voters will have a final say in final pairings and so 2nd place RNKS still matter and is something for the 1st ranked candidate to think about. PVS is best used to deliver a direct and majority connection between voters and choices. The Paired Voting System (PVS) app is designed to provide elections feedback in real time directly to the voters.

5.1 Overview of PVS

PVS is designed to replace all other forms of making decisions and can be applied to shareholder votes, director elections, candidate selections and selections on priority choices as management meetings. Voters state their preferences in RNK order from their top choice of candidate to their last choice of candidate. Each pairing of candidates results in a FOR which applies to one of the candidates, depending on which numerical RNK value was assigned by the voter. If the voter sets the numerical values of each candidate to be the same the FOR is split and they each get ½ FOR. For Each Voter-The sum of the FORS for each candidate pairing is compared. The winning candidate in a pairing is the one who receives the most FORS. The candidate receives 1 WIN if he beats out all other candidates. The Winning candidate among all the candidates is that candidate who has amassed the most WINS. If the WINS are tied then a comparison of TIES is made and if that comparison results in a tie, then the winner is the one that receives the most overall FORS. If that still results in a tie, then the individual FORS each Choice are compared. The top ranked choice or candidate is clearly supported by a majority in this way and each vote counts as 100 percent of votes are in play between the top two candidates. I believe PVS is a great voting concept. I was using it for making decisions in business as early as 2002. It was called stepwise voting at the time and has since morphed into PVS. In 2004 I pitched this concept to the Progressive Conservative party of Canada by sending an email to Peter MacKay with a copy of the prototype program, written in Visual Basic. Although they may not have used the exact same algorithm I provided, they did use this system of voting in their 2004 leadership convention where Stephen Harper was elected leader of the party. PVS clearly and unambiguously reflects the true intentions of the voters and empowers voters to use their best intellectual abilities to focus on and deliver the best decisions. Furthermore, once decisions are made the voters will better support these decisions. The PVS section of this paper focuses on a ranked, paired, system of voting. It sounds complicated but a computerized process makes it quite simple. We will refer to it throughout this presentation as simply PVS. The essence of PVS is that each pairing of candidate choices is evaluated in accordance with the wishes of each voter.

5.2 PVS 1st place rank loses in a direct pairing

It is possible and OK for a top ranked candidate to lose to another candidate in a one-on-one pairing. This is a feature PVS that illustrates hidden relationships that would otherwise go unnoticed.

5.3 Rules of PVS

5.3.1 Analysis of a single pair of choices

The computer compares the RNKS of each voter for each pair of choices and sums them. The number 1 is the highest RNK possible, if a RNK is negative it would be assigned a zero value by the computer. For example, Choices are identified below as X and Ys. The analysis extracts statistics for each pairing.

There is a special treatment for cases where a voter has set RNKS equal to 1 for more than two choices. This will be further discussed below. 1-1-1 1st place ranks are shared among all candidates who received a 1 by a single voter. So, if three candidates were each given a 1 by a voter, they would each be assigned 1/3 1st Place RNK.

5.3.2 Analysis of all pairs:

Statistics are calculated and summarized for all Choices to determine the number of WINS, LOSSES, TIES for each choice. FORS X > FORS Y (e.g., X: 5 FORS, Y 1 FORS) X:WIN=1 ; Y:LOSS=1 FOR X = FOR Y (e.g., X 3 FORS, Y 3 FORS) X: TIE =1; Y: TIE=1 Once all paired choices are analyzed the overall number of WINS, LOSSES,TIES can be compared, and the final rankings established. The overall ranking of the choices is established by comparing the number of WINS as follows.

All Pairs - the main comparison between Candidates is the number of WINS each Candidate receives.

IF a pair of choices are Ranked the same on WINS a comparison can be made based on the total number of TIES registered for each candidate against all other candidates. If these comparisons result in a TIE then we can compare TOTAL FORS each candidate received. If this still results in a TIE then Choice Ratios can be compared and lastly FIRSTS.

5.3.3 Here is an example:

In this example there are only 4 voters. And five choices. Hence the voters get to set RNKS for 4+3+2+1 = 10 pairings. EG for Voter 001, (AB,1:5), (AC, 1:3), (AD, 1:2),(AE,1:4), (BC, 5:3), (BD 5:2), (BE, 5:4), (CD, 3:2) (CE, 3:4), (DE, 2:4)and so on. The RNKs generate a total of 10 FORS resulting from all pairings combined. In this case 4 FORS are attributed to A. The total number of FORS that could be registered for one candidate would range from 0 to 16 depending on how many pairings were won. In the example Danny was RNKed 1 by all voters, he gets 16 FORS.

This is a different election with different RNK values:

The field highlighted in Green provides the tipping point for the 1st place ranking. • Danny has 1 first place vote and Joe has 2. • Danny has 3 WINS. Joe has 2 WINS, so Danny is ranked No 1 • Danny is tied with Joe using choice ratios.

5.3.4 999 Voters:

In the next example we increased the number of voters to 999 and simulated an election once more.

Interestingly, if this were an FPTP/SVS election we would only count the 1st place votes and Leon would have won with 207 1st place votes and 20.72% of the vote (207/999).

We now provide the results of the elections. Donald Ranks 1 in the election with 4 WINS. In the final pairing his choice ratio (support )is 50.65%. Results are remarkably close as this is a completely randomized vote.

5.3.5 PVS allows for equal RNKS to be placed:

And then here is an example where we have two matching 0 values. Recall there is no action taken when a pair of zeros line up. So, there is a lower count of total FORS equal to 39 and not 40. Pay attention to the winners here and the Rank.

5.4 PVS has no proportionality

The argument is made for PVS, that a majority (never a minority) of voters support the number one ranked choice. This reflects the process and the way that ranks are established.

There is some flow-through of representation through this process. The elected representative realizes he must rely on a broader base of support and not just the support of those people that come out in favor of the party platform he is affiliated with. It is only in the Top Pairing that voters would be expressing their final wishes for the top candidate or for the second-place candidate. The winning candidate knows that all voters either cast a vote directly for him or for the 2nd place candidate. If elected using PVS he would not know specifically who his supporters were. He would be more inclined to make decisions based on what is best for the whole constituency instead of pandering to a minority group. This is a subtle but key point because buried within the majority who produced a number 1 ranking, there are other supporters not a part of the candidate’s base. For example, suppose if the final, and most important candidate pair consisted of Conservatives and Liberals. Does the winning candidate really know where the NDP, the Bloc Quebecois and the Green party votes went with respect to the Final Pairing? The recapture of votes that would have been lost in a “First Past the Post” system is applied to the Final Pairing. PVS increases the power of the voters and the accountability of the elected representatives.

5.5 PVS Allows for the expression and consideration of all paired choices.

Voters are free to confidently vote for their true preferences. This is the optimum position to fully support their choices. There are no lost votes because each voter may take part in every pairing.

5.6 PVS provides for an election with many candidates and no split votes.

Because all voter preferences expressed as RNKs are on the table there is no need for strategic voting with respect to split votes. Most jurisdictions hold elections with more than 2 candidates. How is it ever possible to really consider what the voters really want if voters can only vote for only one candidate? PVS solves that problem nicely. The results will always reflect voter intentions. Not some of the voters, but all the voters. No vote splitting, no strategic voting, no vote manipulation. Every voter has a say in the final candidate selection, and the Top Pairing results in a candidate backed by a majority.

5.7 Quicker and more accurate selection of multiple choices

PVS automatically provides a final rank order of choices and so PVS is ideal for selecting a group of acceptable choices. Since PVS is set up to factor in voter weights, its use would be ideal to vote in a slate of directors. One would not even have to contact potential directors prior to a vote taking place. Just put every potential director on the slate and then only if elected ask him/her if he/she would be willing to serve. If not go to the next candidate. If the shareholders disclose the rank order, candidates obtain e clear feedback as to where they stand with the shareholders. Interestingly the directors could participate in such a vote to establish slates for the shareholders. At the same time, the ranking of directors would provide helpful feedback for the existing directors.

5.8 True democracy

A government elected by a clear majority is a true democracy. Provided a WDC choice is included PVS guarantees, majority support of the elected candidate. If the logical extension to PVS provides for elevation or proportionality, then the democracy would be further strengthened.

5.9 PVS is the first step:

PVS extracts RNK data for individual candidates, ridings, and parties. The PVS database provides data concerning Choice Ratios, candidate ranks, first-place votes, and other PVS data. This data can be used to drive Proportional Representation in whatever form it may be.

6 PVS -Step by Step:

6.1 User Preferences

6.2 RNK Evaluations:

6.3 WINS:

6.4 TIES:

6.5 TOTAL FORS:

6.6 DETAILED FORS:

6.7 FIRSTS:

6.8 CHOICE RATIOS:

6.9 RANKINGS:

6.10 Rank Order:

7 PVS Model Canadian Riding:

^[6] The relevant excel file is entitled: PPWVS 20220810.xlsm It is digitally signed by 4RP Canada Inc .

This model simulates PVS over 338 ridings. Some of the information in this section is technical and can be skipped. This is up to the reader to decide. This example uses Riding 6 St. John’s East from the 2015 Canadian Federal Election. In riding 6 there were 44,880 voters. As it was the Liberal party candidate was elected by a minority of voters.

The object of a randomized vote is to use the results previously obtained to generate a hypothetical voting situation where all 44,880 voters contributed to a PVS scenario. By examining the summary of these vote results we can see that when PVS is used some of the smaller blocks of votes transfer over to either the NDP or the Liberal party and create a different result.

7.1 Review the variables:

VB module BGlobals20180321 : This module identifies and defines variables set in place to drive the simulation.

7.2 Create ridings:

VB module Acreateridings201803101 Execute subroutine CreateAllRidings() Create one blank riding to start the process. In my example I started out with a blank riding having room for approximately 10 candidates. Once this blank riding was set up, I ran the program to set up 338 ridings and then deactivated this subroutine to prevent overwrites.

7.3 Populate Ridings

Sub CreateAllRidings() Populate the ridings with information from the election you wish to simulate. In this case I used the results of the 2015 Canadian election as the base case for the simulation. This is a tedious process and involves loading in all 338 ridings with the candidate names, the number of votes attached to each candidate, the parties associated with each candidate.

7.4 Execute a PVS vote for each riding.

There are two ways to conduct the PVS portion of the program.

7.4.1 Process RNKS by setting up RNK blocks.

The first way was to populate an RNK block containing all the different combinations which provides for the weight assigned to each combination of votes. Partial shot is shown below: Sub MainvotingProject() This subroutine execution completes the PVS calculations and sets up the data from which final election results are developed for each riding. A data set consisting of one voter forms a microcosm of what makes up the final total. The computer simulates an analysis of the complete riding. The basis for the simulation begins with some actual results from the 2015 election:

For the simulation, the following table identifies typical RNKS placed by one voter.

The computer repeats this process for 44,880 different voters with different selections processed in accordance with the random processes previously assumed. The following partial display is for the Riding 6, RNK Block The idealized one voter scenario would have been the most common and would have come up approximately 11,767 times as shown in the attached excerpt of the results table. Due to the number of variants, it is not possible to show all the possible combinations in this clip shot.

7.4.2 Process RNKS by direct calculation.

A much faster technique sets up a digital array and processes each voter’s randomized and skewed RNKS individually and then transfers the results to a digital data array for further processing. Sub subDirectCalculation() 'These calculations set up an array in the digital memory of the computer. 'Each voter’s votes are processed one at a time and tallied up fill summary blocks 2 and 3. 'Each time the subroutine is called is called by an individual riding. In our example , we are looking at riding 1 in the 2015 , Canadian Election.

7.4.2.1 First place RNK:

As you can see in the clip shot below the starting percentages of first place votes are indicated. These are shown for each of the 338 ridings. Using this as a starting point for the simulations, one can randomly select votes such that approximately 55.9% of the first-place votes go to the Liberals. And then so on down the line. For each voter we assign an initial random number which identifies his choice for first place RNK:

Consider the effects of applying various random numbers to generate the following table.

100 random numbers were picked and the results for the first place RNKs of 100 voters are tabulated.

7.4.2.2 Example 2nd place RNKS

Now assume the voter has picked the Liberals as his first choice. The voter as per the simulation now will pick his 2nd choice from the remaining pool of candidates. The randomized RNKs in this example are designed to utilize the same relative strengths of the remaining candidates to select subsequent candidates.

This is a bit of a stretch as various scenarios can be presented here and in the real world this relationship would not hold. PVS is especially important as it releases the true intents of the voters. This simulation serves the purpose only of illustrating the PVS concepts which were applied in the models.

Example selections

Summary of 2nd place RNKS for 100 voters where the 1st place RNK was Liberal.

7.4.2.3 Third place RNKS:

The voter has picked out, the Liberals and the NDP as his first and second choices. The voter as per the simulation now picks his third choice from the remaining pool of candidates.

This approach is a reasonable way to form the example basis for the third choice RNKS, I will use the same percentages that were developed in the actual 2015 election to move the RNK selection to the third place. The results are as follows.

Results of third place vote

7.4.2.4 4th and 5th place RNKS:

After the hypothetical voter has selected the Conservatives as his third choice only the Green party and the Communist Party are remaining. We ran through the scenario again.

AND

We conclude, for the purposes of this simulation the voter chooses Green as his fourth choice. This leaves the Communist Party as his fifth choice. Summarizing voter rankings for 1 voter:

Final rankings are based on voter RNKS built up of individual random rnks of all voters.

7.4.3 Global WINS, Ties and Losses

Sub subPopulateResultsBlock3() Based on the pairings of all choices and comparing RNKs, as discussed earlier, the following results table can be set up.

7.4.4 Completing the Choice ratios:

This table of individual FOR results is generated from PVS RNKED pairs analysis.

The next logical calculations set the ranks and calculate the Choice Ratios.

Total possible FORS =44880 12.56% = 5637/44880 48.97% = 21979/44880 51.24% = 22995/44880 2.35% = 1054/44880 0.65% = 290/44880 The choice ratios set the stage for proportionality calculations and represent the relative strengths of the 1st ranked candidates compared to all others. Exactly how this proportionality works and is managed is covered elsewhere in this paper.

8 PPWVS Paired Proportional Weighed Voting System

8.1 Proportional Voting

There is a strong worldwide interest in Proportional Representation. Voters are concerned about lost votes, minority elections, inferior representation, and no representation. This paper focuses on two paths to deliver Proportional Representation. In a multiparty system, proportionality may create difficulty for any one party to reach a clear majority. This may be a problem in some people’s eyes and could affect governance. I do believe the use of PVS combined with PPWVS in the legislature makes these problems go away. Should a form of Proportional Representation be put in place, a majority party coming from any form of non-proportional voting will see their power change. An elected prime minister (under FPTP/SVS) can leave an intelligent and thoughtful legacy when he/she leaves office by implementing electoral reform which includes PVS and Proportional Representation. There are ways to channel votes to achieve proportional results. Paired voting system (PVS) ranks the candidates in order of top to bottom. The PVS elected candidates in a normal election go on to represent their ridings in the legislature. PVS also generates data to drive a form of proportional representation if such is desired and this may result in demotions and elevations of candidates.

8.2 Better representation:

PPWVS (Paired Proportional Weighed Voting System) increases voter power and candidate accountability. Intention and voter power are better distributed at the legislative level. By having two streams of voter power, voter desires, both locally(candidate) and globally(party) are better represented.

8.3 Proportionality Uplifts from Choice Ratios 1st and 2nd Place Candidates.

8.3.1 1st - Preferred option PPWVS - Weighed votes:

Each candidate in a party has an equal vote Instead of elevating or demoting candidates the option would be to assign weights to elected candidates to reflect the proportionality as pushed up by the Choice Ratios. This would be done on a party basis. In the simulation of the Canadian election the sum of the First Place and Second Places Sums of choice ratios for the Conservatives was 109.7761. However, without elevation there would only be 99 candidates. Those 99 candidates could be left in place and instead their votes would count as 1.11 each.

In the example shown above there are 99 Conservative candidates locally elected and each of their votes would be assigned a weight of 1.11 at the legislature.

The votes would have to be studied a bit to see what practical rules for a show of hands could be used prior to a definitive computer vote being needed. It would be practical to have computer voting done online using logons for candidates. Logons could be biometric in nature. Records of votes taken could be displayed on larger monitors to ensure the process is transparent. The total number of votes is based on 338 ridings.

8.3.2 2nd - Preferred option PPVS: One candidate, one vote.

Elevate or demote candidates to reflect the proportionality as pushed up by the Choice Ratios on a riding-by-riding basis. This would mean that each candidate would be able to hold one vote in the legislature. This option would mean demotions and elevations which are politically problematic but would mean a simple show of hands at the legislature for voting purposes which would be easier to administer.

9 PPVS/PPWVS Computer Modelling

This section reviews the model using a real-life example. There are relevant functional excel programs located at the following location: PVS Voting Documentation along with other relevant information. This is made available by the author for testing and use.

9.1 Targets:

^[7]

The targets of the PPVS/PPWVS model relate to the real-life election which was used to drive the simulation. Since the whole basis of Proportional Representation is to respond to the political power of all voters including previously underrepresented voters and parties it will come as no surprise that PPVS/PPWVS takes care of this issue. In the October 19th, 2015, Canadian Federal Election, the Liberals secured 184 seats, the Conservatives secured 99 seats, the NDP secured 44 seats, the Bloc Quebecois secured 10 seats, and the Green party secured 1 seat.

These and the detailed historical results from each riding form the basis for the computer model.

9.2 Rules for PPVS/PPWVS

9.2.1 Each riding carries a total weight of 1 in the legislature.

9.2.2 PVS generates the rank order of candidates.

9.2.3 Focus is on first and second place candidates:

In the model voters have a RNK vote with respect to all candidates and parties running for election and the ones that are considered in the final proportionality analysis are for the top ranked pairing only. Although there may be disagreement on this method, my feeling is that if a candidate does not make it to either the 1st or 2nd place rank then no weight needs to be given to the FORS in favour of that candidate and his party. The line must be drawn somewhere. Voters need good solid representation. Thus, provided a voter’s RNKING has generated a FOR in favour of either the 1st place candidate or the second-place candidate the FOR will be counted towards the proportionality calculations. The only exception to this would be where a voter has RNKed a second-place candidate in a riding, and that second-place candidate has no party affiliation with a party that elected a candidate. That would be termed a wasted vote. In the model the percentage of wasted votes in the above fashion is .058%. 99.94% of voters are represented at the legislature, one way or another. In FPTP/SVS the electorate is lucky to have over 50% represented at the legislature. In the odd case where a candidate with a 3rd place rank is elevated his voting power will come from proportionality elevated from elsewhere. It is a trivial thought experiment to imagine the negative implications of assigning weights from FORs generated for 3rd and lower place ranked candidates. Where the ridings have different numbers of candidates this problem would be significant. Elevation of third place candidates is only possible but only if they meet the Minimum Choice Ratio criteria and where 1st ranked, and 2nd ranked candidates can be demoted due to proportionality considerations. Since the sum of the Choice Ratios for the 1st and 2nd place candidates = 1 then each riding is represented as having a weight of 1 when proportionalities are applied. We should not go down a path where proportionality is applied to the legislature based on the number of votes in a riding as opposed to unity of the riding. Some ridings are small, some are spread out. All my thought experiments and simulations previously made do not provide for a positive proportionality outcome unless the riding is provided with the weight of 1. Proportional Representation will be based on the sum of Choice Ratios collected by candidates who have placed in either first or second position. All voters have a say in this Final Pairing. All they need to do is RNK their choices.

9.2.4 Only Elevate where the Choice Ratio spread is less than 10%

What level can and should an elevation take place? For example, if the first-place candidate has a Choice Ratio of 75%. This means that the second-place candidate will have a Choice Ratio of 25%. In a count of 100 votes the first-place candidate would have received 75 FORS and the second-place candidate would have received 25 FORS. It is a poor idea to elevate or demote in such an instance as the disparity is too great. On the other hand, if a first-place candidate had a Choice Ratio of 51% and the second-place candidate had a Choice Ratio of 49% then an elevation and a demotion would seem to make clear sense if needed to preserve proportionality for the respective parties. If I were the first-place candidate and had a Choice Ratio of 51% I might not like it but would accept it if those were the rules. A second-place candidate with 49% support still has a lot of support in the riding, The model uses limits of 55% -50% for demotions and 45% to 50% for elevations.

9.2.5 Minimum Proportional Representation:

To participate in Proportional Representation a party must achieve at least a Proportional Representation summary of 1.

9.2.6 When proportionality numbers are not met weights must be used.

Proportionality by elevations and demotion requires some spilled political blood at the riding level. This comes in the form of demotions to candidates elected under PVs as per proportionality requirements. Demotions are impossible to avoid unless one applies vote weighing to the candidates. If the requisite number of elevations and demotions are not met, then the legislative votes will need to have weights applied or alternatively some lack of proportionality must be tolerated, and the best decisions made under those circumstances. This is what the election looks like before proportionality is applied and with no demotions or elevations.

9.2.7 Parties must have an elected representative:

Party Proportional Representation in Parliament would be through an elected representative even if such an election occurs as the result of an elevation.

9.2.8 Digital identification may be used:

A computer could verify a parliamentary elected representative’s right to vote. There are various biometric ways to do this including facial recognition, voiceprint, fingerprints, iris scans. In addition, there are digital codes that could be input into a representative’s computer terminal or digital device application of some kind. With the use of computers votes can be in real-time and documented.

9.2.9 Voting where there are only two Choices, A and B.

This would be the easiest way to set up a vote. The speaker of the house would ask those in favor of choice A to stand up. The computer would digitally recognize all standing persons and apply the weighing factors which would be displayed on the monitors. The FORS would be totaled up for that choice and if a majority of FORS are obtained the choice would be carried. If a majority of FORS are not obtained, then the same process could be repeated for Choice B. Again, if a majority is obtained Choice B is passed. If neither A or B were carried with a majority then neither option would be selected, and it would be back to the drawing board and no decision is made.

9.2.10 Voting where there are multiple choices such as A, B, Do Nothing, WDC.

The list of choices would be set up on each representative’s device and they would RNK their choices. Once the voting is complete PVS would be digitally applied to rank the choices. If applicable at that time weights could be used In any case as many choices as the legislature wants to vote on can be tabled to fine tune options and reach consensus faster.

9.2.11 Built in Constraints:

There will need to be reductions or increases in the number of candidates for a given party based on Proportional Representation. Some candidates might be elevated to elected status and some candidates might be demoted from elected status. There are manageable problems where a first-place candidate is demoted in favor of a second-place candidate. The built-in constraints for the program are no promotions will take place unless the second-place candidate has a Choice Ratio of at least 45%. The computer program automatically begins the process of elevation with the closest results first to ensure that any elevations/demotions that take place make the most sense.

9.3 Execution

9.3.1 Candidates are ranked using PVS.

A summary of all candidates is prepared and sorted by their respective Choice Ratios from the highest to lowest.

9.3.2 After PVS the program Populates the Choice Ratio Summary Worksheet

Sub subFinalSummary() ' populate the final summary.

The inclusion of this data as part of the worksheet calculations provides an understanding of how the proportionality analysis works. The candidates are sorted in descending order from the highest Choice Ratio to the lowest Choice Ratio. This will conform in most cases (See the Condorcet Exception) to the Rank Order as established by PVS. I estimate that the chances of a Condorcet non-conformance is extremely low given that elections and choices invariably always produce skewing of the results in the direction of the favored candidates and parties.

9.3.3 Populate the initial ProCalcs tables:

Call subRunElections_4 For intcandidateAll = 1 To gcintNoOfRidings For those of you who are knowledgeable of computer language the preceding FOR statement runs through an initial election process without any proportional adjustments, demotions, or elevations. It just looks at the final ranking summary table and considers only the first 338 candidates which are ranked number one in their respective ridings. Note the shortfall in Conservatives elected locally and a surplus in Liberals elected locally. The intent is that once proportionality considerations are considered the achieved proportional change will match the planned proportional change and will yield elected numbers that are equal to the allocated candidates.

9.3.4 Details on the Procalcs Spreadsheet

• First Place and Second Place Sums of Choice Ratios Proportionality uses Choice Ratios carried by the first and second place candidates in each riding. This proportionality is applied to the parties and sets the final number of allocated candidates. This is an important concept to understand and if you are reading this and are unclear about what the Choice Ratio is and how it works, I kindly refer you to the definitions section of this document and the part of the document that deals with PVS. • Allocated candidates. The final numbers are tweaked and rounded out to zero decimal places, so the sum of the allocated candidates is equal to the number of ridings. • Elected c/w elevation and or demotion. This column is left blank for now pending the execution of the phase which elevates or devotes candidates to achieve proportionality. This will be explained later. • Achieved proportional change. The achieved proportional change should bridge the difference between those locally elected numbers and the allocated numbers. It is possible that after completion of the phase II calculations a proportional result occurs, and it does not comply 100% with the intent. In the example shown above the intention is to elevate enough Conservatives to fulfil their target mandate of 111 seats. • Planned proportional change. At the end of the stage II process the achieved proportional change should exactly match the planned proportional change unless it was not possible due to the exact configuration of the election. This is unlikely to occur but if so, it would mean the proportionality would be slightly off but not by much. • Locally Elected no Elevation or Demotion EG Conservatives in this example 99. This would be the results based on PVS in each riding. Proportionality is not considered and there are no elevations or demotions of candidates. So, this is completely a result of the PVS process.

9.4 Searching for a candidate to elevate.

9.4.1 Sequence of processes to Elevate and Demote.

Each 2nd place candidate’s riding is examined in turn processing from the highest choice ratio to the lowest choice ratio. The computer checks whether the candidate under consideration has more than the Minimum Choice Ratio to enable an elevation. If not, the computer program will not look at any more candidates on the list. If the candidate’s party has a shortfall s as determined by proportionality and if the 1st ranked candidate’s party has a surplus in elected numbers, the first-place candidate can be demoted, and the second-place candidate can be elevated. Once all elevations and the motions have been conducted there will be a balance at the legislative level that closely approximates the values provided by considering the uplifted proportionality-based contributions of the Choice Ratios. In the simulation and before elevations and demotions the Conservative party had a shortfall of 11 and the Liberals had a surplus of 22 members.

Both Tim Uppal, and Amerjeet Sohi are in riding 276. Mr. Sohi was elected in a close race. The Choice Ratio for Tim Uppal is 0.49991, which means that out of 10000 votes cast for the Final Pairing between himself and the Liberal candidate he would have received 4999 FORS for the Liberal would have received 5001 FORS.

It is a simple matter for the computer program to elevate the Conservative and demote the Liberal and in this case Riding 276 now looks like this.

The last elevation where MCR =.4666 was in riding 47. This example shows the largest separation between two candidates and what some of the relevant thoughts are.

9.4.2 Interim results Final Summary table Partial screen:

This is the breakdown for the Elevations and Demotions of the Conservatives and Liberals.

The program is set up to perform elevations and demotions in sequential order starting with the smallest separations which means that the strongest candidates are always given preference to maintain their first-place positions.

9.5 Final Proportionality Calculations Table PPVS

The Conservatives have 99 elected. The Proportional calculations show they should have 111 positions sent to Parliament. There will be 11 promotions of Conservatives. The Liberals have 844 elected. The Proportional calculations indicate that they should have 162 positions sent to Parliament. The result was 22 demotions. The Green party has 1 elected. The proportional calculations indicate they should have 1 position sent to Parliament. No demotion or elevation is required. The BQ has 10 elected. The Proportional calculations indicate that they should have 10 positions sent to Parliament. No demotion or elevations were required. The NDP has 44 elected. The Proportional calculations indicate that they should have 55 positions sent to Parliament. This resulted in 11 elevations. No Affiliation candidate(s) has 0 elected and uplifts rounded off come to 0. This results in zero candidates being elected by elevation. As there was no affiliation with any party, and so RNK votes cast for these candidates will not be represented in Parliament as there are no voices that can speak for them in the legislature.

9.6 Elevations and Demotions summarized:

To meet their proportional numbers 11 Liberals were demoted in favor of the NDP as follows:

And 11 demoted in favor of the Conservatives as follows:

9.7 PPWVS weighted votes:

PPWVS does not elevate or demote candidates. Each elected representative is given a proportionate share of his party’s proportionality uplifts.

As one can see from the example provided, a majority by show of hands would occur in a range of 148 hands to 187 hands to definitive support. Anything in the range of 148 to 187 hands will require the proportional weights to be considered. If the number or hands were over 186 or under 148 then one could bypass a digital process. For the day to day running of the house, the assembly can effectively deal with these constraints by using a show of hands when a clear consensus is in play otherwise using a more detailed, and digital weighed count of the votes. This would happen only if there was a contentious issue.

9.7.1 The strength of PPWVS (Paired Proportional Weighed Voting System)

PPWVS does not require an adjustment in the number of elected representatives based on proportionality, but instead can provide for an adjustment to the voting power of each elected representative based on the numbers of FORS tallied, (as per Choice Ratios) for each 1st and 2nd place candidate. Every FOR will count, through proportionality. Consider where a voter RNKed a Conservative candidate ahead of the Liberal candidate, and the Liberal Candidate was elected with the Conservative candidate coming in second place. The FORS for the Conservative candidate will still count through proportional uplifts being transferred to other Conservative candidates who were elected. This achieves the goal of proportionality in that all FORS collected by either a first or second place candidate will be in play in the legislature when votes are cast. Voters push their political power up to a legislative assembly in a coordinated manner with the important voter party preferences in play by virtue of the FORS which arising from RNKs. PPWVS (Paired Proportional Weighed Voting System) increases candidate accountability as opposed to FPTP/SVS. Voter power flows up to the legislative level with very few lost votes. Two streams of voter power, voter desires locally(candidate) and globally(party) are represented at the legislature.

9.7.2 The weakness of PPWVS

PPWVS will be resisted by politicians and voters who are unwilling to share political power even if it is better for the country. Some people do not like change. Many will not understand the proposed process or trust it. Some will trust the process but pretend not to order to promote some hidden agenda they might have. This is complicated because people are complicated. In the legislature, some people would be skeptical of voting on decisions which require computers doing some of the calculations. The skepticism is misplaced. In most instances a show of hands would be quite appropriate to make the decision. Where necessary and for more complex decisions, a computer PVS vote would ensure decisions reflect the weighed wishes of representatives and keep proper records at the same time.

9.7.3 Voter strategy PPWVS:

This is a one voter strategy. Given that there is a great variation in voters, it is not possible to set out a strategy that will work for everyone. Go through the list of candidates on the ballot and pick out the candidate, whose party will best represent your interests and the interests of your riding and country. Put a 1 in the box beside that candidate’s name. Go through the list of candidates on the ballot and pick out a candidate who you feel will best represent your interests and the interests of your riding irrespective of party affiliation. Put a 2 in the box beside that candidate’s name. Go through the remaining list of candidates. Your next preferred candidate will be a 3 and so on A voter may RNK both candidates the same when he/she perceives them as being equal. RNK a candidate as a 0 and he places after any RNKed candidate who is RNKed non-zero. Use RNKs on all candidates, to show support for your preferred candidates in the Top Pairing of candidates. Because of PPVS’s proportional nature, first and second place candidates will always have a voice at the legislature through the parties the candidates belong to. In addition, because of the RNKing of candidates, each candidate and party who are elected will feel a duty of responsibility to all the voters. The pandering to minorities by an elected candidate will not be helpful to get re-elected. PVS and the Proportionality extensions of either PPVS or PPWVS will inspire candidates to be more truthful when trying to get elected.

10 Examples

10.1 PVS Randomization of a simple model:

Randomization assumes the order of the Voter rankings (RNK) will be from 1 to N, where N is the total number of candidates. Each choice RNK is assigned a random value from 1 to N. Sample with 999 voters and 7 choices. PVS gives us the ranks for the candidates and choice ratios provide the drivers for proportionality. Step 1 Run the numbers:

Step 2 analyse and obtain the results.

10.2 PVS General decision-making:

PVS can be used for general decision-making where alternative choices must be decided. Suppose a motion must be tabled to decide on a budget amount for a certain research project. Normally after a substantial amount of arm wrestling a budget amount is put on the table and voted on yes or no. This invariably leads to some people being disenfranchised from the decision as they all have different opinions and to be brutally frank sometimes the person with the biggest mouth or the strongest political position gets his choice put in front of the team for a vote. This really upsets some people whose logic has been upended by someone else’s emotionally laden and illogical rhetoric. PVS provides for each person’s choice to be and put on the table. RNKing the choices and producing ranks means no one is left out of the decision-making process. Furthermore, unacceptable choices can be firmly and decisively ruled out by the voters. In addition, people can see how their choices are really being evaluated by others in the group. Learning experiences. Also See https://en.wikipedia.org/wiki/Ranked_pairs

10.3 PVS 6 choices and 1000 voters:

These are completely random over a wide selection with none of the voter bias found in a typical election. Therefore, the results are close.

Result Cruz has 5 WINS and 0 LOSSES and so is a clear winner. We can examine the data more deeply to see what else is going on. Cruz has no losses and so is on top of all other candidates in terms of FORS but not in terms of 1st place RNKs. Again, the case for throwing out FPTP/SVS is made just look at the 1st place RNKS.

It is highly unlikely, but theoretically possible a choice may be ranked(PVS) first over all other choices but might have a LOSS as well. This is a mathematical possibility in a real election, but unlikely because of biases introduced by voters in favor of certain choices. In randomized simulations A Condorcet error is possible. Do not make the mistake of confusing the two, as all elections have a clear bias whereas not all simulations do. Properly executed elections are meant to tease out the biases in favor of the best candidates.

10.4 PVS Board Elections:

10.4.1 Stacking boards with minorities and gender differences.

• PVS allows shareholders to RNK their preferences for all candidates. • The weights attached to each shareholder will ensure the full power of each shareholder’s voting rights. • PVS generates a list from the top ranked to the lowest ranked candidates. • Board members would be selected in order of their final rankings. • Minorities can be selected until the minimum numbers are reached. • Candidates can be approached in rank order and asked if they will allow their names to stand. If a person accepts then they become a board member. If a person does not accept the procedure is repeated until a full slate has been filled. • There would be no need to approach candidates in advance of the RNK voting. Say that it has been predetermined that a minimum of two females would have to sit on the board to meet statutory requirements in the relevant jurisdiction. Starting at the top of the ranked list we would see that Lucy would be sitting on the board as one of the original directors. That is fine. The next female on the list would be Nancy SNB and she would be approached and asked to sit on the board. Unfortunately, by putting Nancy on the board Barry SNB would not have to be approached to let his name stand. One can easily see that minorities can be easily accommodated using PVS without unduly derailing anybody’s sensitivities. ===10.4.2 Directors vote for their own slate===. In many cases it is the directors who produce the slate of possible directors. This slate is then presented to the shareholders. The directors would be highly knowledgeable of the contributions existing directors make to the overall direction of the enterprise. They should be provided with an opportunity to RNK their peers but at a slightly different stage of the process and with a different goal in mind. Their goal should be to provide a slate of and ranks of directors which would be loaded with meaning for the shareholders to consider.

10.4.3 PVS Board Election Example:

Suppose a board has 5 board members. It has come time to recommend a slate of candidates to the shareholders. Each board member nominates a name for possible inclusion to the board that is not a current board member. The current slate of directors is included in the voting pool. There is now a director voting pool of 10 candidates possible for director positions. EBM = Existing Board Member, NBB = Nominated by Board. SNB = Shareholder Nominated

The next step is to have the board vote on the slate using PVS. I have not included WND (will not do) choice as there may be some people that would not be voted onto the board under any circumstances because I am assuming there are enough valid choices not to worry about this option. It would be an embarrassment for someone if they were ranked below the WND choice so maybe it is best to avoid this message even though some people would benefit from such a message particularly if they are particularly unsuitable for a board position.

10.4.4 This is a sample PVS vote where the directors RNK their candidates.

The computerized analysis then takes place and yields the following ranks.

Note that three candidates nominated by the Board rank in the top three.

Let us assume for the purposes of this calculation and as a prequel to the next step that they have been approached and out of the three Harry and Zeke agree to serve on the board, but Eric declines a position on the board. Bruce and Charlie are not approached because they are too far down on the list. The slate the directors below is sent to the shareholders.

Shareholders can also nominate their own people to the board. And so, the names the shareholders have provided are added to the list. There are three people added by the shareholders and the existing board members all let their names stand on the board. The slate presented to the shareholders is determined to have a 10 people on it. 5 of them are the original five board members plus two possible new board members nominated by the existing directors, plus three possible new board members nominated by shareholders. This forms a new list as follows:

10.4.5 The list is presented to the shareholders for the final vote.

Transparency yields a more effective board because the shareholders are given an opportunity to see how the directors view each other and this would influence their vote for the better. There are those who would argue that such a ranking would lead to a popularity contest. I disagree. Most directors are conscientious in their jobs and popularity without respect and productivity will yield an unsatisfactory rank for a candidate while the reverse is also true that if a director does a decent job, he would be recognized for it. For the purposes of this example, I assume 10 voting shareholders. Each shareholder might represent a different voting block and so I have set up shareholder weights to reflect such a possibility. There can be as many shareholders as are required to vote. And so here is a possible table showing the shareholder weights and possible votes before the results are calculated.

Once the votes have been collected the vote takes place in the computer analysis yields the following results.

And then pruning the list Unless a person has already agreed to serve on the board the process that follows would start with the number 1 person on the list being Lucy. Each person would be offered a position on the board commensurate with his ranking on the list. If a person does not want to accept a position on the board commensurate with his ranking on the list, he may choose not to let his name stand. In this example Donald, who has been nominated by shareholders as a possible new board member is approached and he agrees to let his name stand.

1 Lucy EBM is an existing board member and has already agreed to remain on the board.
2 Harry NBB is a new board member who has already been vetted and he is approached and agrees to let his name stand as a new board member.
3 Donald SNB is approached and lets his name stand.
4 Sam EBM is an existing board member and has already agreed to remain on the board.
5 Barry SNB is approached and allows to let his name stand.
6 Danny EBM, Zeke NBB , Nancy SNB , Joe EBM , Leon EBM did not make the final cut.
7 Nancy SNB and ZEKE NBB do not need to be approached.
8 Danny EBM, Joe EBM, Leon EBM need to be contacted and provided with regrets as they have been replaced as board members.

And the final vetted list would look like this:

I am not sure if people would be comfortable if shown a final rank of 8 for Nancy or even showing the ranks at all to the public or to the shareholders. Once the five are chosen they will become equal as directors. This point could be a focus of some discussion. I would support full transparency but there are others that may not be comfortable with that. It seems important to me that people can RNK confidentially but that the final rankings should be made public. Some may wish to entertain some form of proportionality using PVS data.

10.4.6 Discussion of Director Elections

It is a struggle to adequately explain the ramifications of what these outcomes mean in terms of the different messages resulting from this. First, if you are a person who was sitting on the board the final rankings give you feedback of what level of contribution the other board members think you bring to the table. This gives you an opportunity to reflect on your contributions in terms of your suitability for directorship, whether you bring enough value to the position, and whether you are properly placed in the pecking order of the board. There is nothing wrong with knowing your place and living with it even if it means having to leave the board. Indications of value to the non-deserving diminish the deserving and vice versa. Who wants a board where everyone is treated equally and old Mitch in his wheelchair and oxygen mask is kept on just because there are no clear criteria for removing him? Obviously if there are 20 candidates vying for 10 positions there will be some eyes opened. Every time a vote is taken for a slate of directors using PVS it is an opportunity for a form of 360 analysis which provides an opportunity for people to know their place. At that point they can accept their place or take whatever steps are required to change it. I am not sure if the average director would be willing to obtain a frank assessment of where he or she stands in the pecking order and so it is with some trepidation that I make these recommendations. The clear advantage of directors stepping in and voting on the initial slate is that possible directors do not have to be approached in advance to see if they are willing to accept a position on the board. If their name comes up as one of the choices that is to be selected in the final shareholder vote, then one can simply apprise them of the specific director requirements of the enterprise and ask them if they are willing to sit on the board for established terms of renumeration and compensation. They can then choose yes or no whether they want to sit on the board, and it ends there. There does not have to be a long-complicated song and dance before the actual voting of RNKS takes place. There need not be pre-negotiations to ask potential directors whether they want to sit as director or not. Shareholders can nominate potential directors prior to the shareholder RNKS, and it would be up to them to provide a bio of prospective candidates that can be shared with other shareholders in any listing of possible directors that is handed out.

10.4.7 A Board Election of its own Chairman:

The directors could use PVS to elect a chairperson for themselves. This would be an interesting process in that for the Chair to be selected he would have to have the majority support of the board. Sometimes the most highly thought of people on boards and those that might be most effective are not the biggest loudmouths.

10.5 PVS Budget votes:

Suppose the government needs to make a budget choice to try to decide what their budget deficit or surplus should be for the year. Every member of the legislative body represents different constituents and is entitled to and will have separate opinions on budget amounts. As it now stands, these matters get resolved by backroom deals, maneuvering, political strategizing, forces of personality, threats and so on. After a period of agony and discussion two choices are put on the floor and people vote on them. It becomes a yes or no proposition and you either vote for or against it. In this way a plurality of support bubbles out and whatever choice is voted on has the majority support of the people voting. Any belief that represents an intelligent decision is many times than not an illusion and alas, the reality is often quite different. Here are some ways choices can be manipulated politically. Two choices A and B are provided out of the melting pot of choices that are discussed. Minority political forces strong and vocal manipulate the situation and Choice A is their preferred choice. They set up a choice B that is completely unacceptable. The vote is called and of course choice A is carried. This leaves a variety of others who are left holding the bag about choice C, choice D and so on. I call this the bait and switch. PVS takes a lot of this out of the mix.

10.6 PVS Capital of a Country:

Think of a situation where the legislature is going to make a choice as to where they should locate the capital of a country. Suppose the USA wanted to relocate their capital to one of the following States and there is only one jurisdiction where such could be located. Imagine that each State would vote for the capital to be located firstly within their state and secondly in a state that is the next closest to itself to itself and so on. Where would the capital be located? Where should the capital be located? Top 10 states in the USA ranked by population circa 2015 California 39,536,653 Texas 28,304,596 Florida 20,984,400 New York 19,849,399 Pennsylvania 12,805,537 Illinois 12,802,023 Ohio 11,658,609 Georgia 10,429,379 North Carolina 10,273,419 Michigan 9,962,311

1st Place Results We tabulate the 1st place votes against every other State. It is done for every combination because in some cases there may be voters that will put more than one choice in 1st place which will cause a sharing of the 1st place votes. This will change the values in the table. The 1st place votes are not relevant in PVS unless all else is equal and are shown for the reader to get some perspective.

Next the computer program calculates the FORS that apply for every combination. Comparing California VS Ohio California FOR 39,537 K Ohio FOR 137,069 K Ohio has a Choice Ratio of (137,060K/(39,537K + 137060K) ) 77.60% California has a Choice Ratio of 22.40%. Clearly Ohio is a superior choice for the Capital supported by a full 77.60% of the population of the voting states. If we were to use FPTP/SVS California would win with votes of 39,537 out of a total of 176,606 K. This is a support level of 22%. 39,537/K(176,606k). Results:

California was ranked 1st by population (1st place RNKS) but came in 10th. This is significant because it illustrates that even though; on a comparative basis of population alone California would have the most number first place votes, in actual fact using a flawed approach of considering only the first place votes [i.e. the population] to determine the capital would have resulted in the selection of a California and this would have been the worst choice. Ohio as a state was ranked seventh in population but came in 1st for capital location. Given that the geographic distance can be compared to practical working separation this is a perfectly reasonable explanation. After the vote, all voters obtain the best possible results in terms of geographical separation. This result takes the needs of all voters into account. Okay so now look at this in political terms. Pretend that California is Donald Trump, and he is running against 9 other candidates using FPTP/SVS. He WINS. Congratulations to the ancient split vote system implemented hundreds of years ago which is still ineffective and yields poor results. When California is put up against Ohio in a paired choice it garners only 22.39% FORS. Something similar happens that is similar with an elected candidate. Someone who is off to one side supported by a minority of voters still gets in.

10.7 PVS Managing Ideas out of Corporate Meetings

Consider development meetings to explore innovative ideas, strategies, priorities, and other various choices that might be made. Invariably the moderator lists all the important and different ideas in a series of bullet points. These would be discussed and at the end of the meeting there would be solemn pronouncements of thanks for the contributions of all the attendees and assertions that actions would be taken. In my experience that is exactly when most of the important ideas would be buried. There is always hope for some champion who will discover someone’s especially important idea and run with it and make it happen. I guess in some companies this does happen. There was so much lost potential by not being able to sort and rank all the ideas and act on them in order of real importance. An incredibly significant contribution to the handling of ideas would be to list ideas as a series of bullet points and then use PVS to rank the points in descending order. This would provide a clear focus to move forward with the better points in a priority sequence.

10.8 PVS Block Voting:

PVS lends itself well to block ( or Proportional) voting by inputting the number of block votes into the weights field of the input table. An example can the found-on Wikipedia. This example is adapted from the Wikipedia article on Ranked Pairs(RP). ^[8] PVS operates in a way to take care of the Condorcet possible error and always produces clear ranks of the possibilities.

Tennessee map for voting example

Imagine that the population of Tennessee, a state in the United States, is voting on the location of its capital. The population of Tennessee is concentrated around its four major cities, which are spread throughout the state. For this example, suppose that the entire electorate lives in one of these four cities, and that they would like the capital to be established as close to their city as possible. The candidates for the capital are: Memphis, the state's largest city, with 42% of the voters, but located far from the other cities. Nashville, with 26% of the voters Knoxville, with 17% of the voters Chattanooga, with 15% of the voters The RNKs of the voters would be divided like this, based on distances.

The results would process out like this:

And the outcome.

If the matter were decided by FPTP/SVS voting the capital would be in Memphis. FPTP/SVS would consider only the top RNK for the candidate cities. Clearly this would not represent the wishes of a majority voters and PVS clearly yields the best result, which is Nashville. In the Wikipedia example…. Nashville WINS as wells. The logic is the same. In a direct comparison of Nashville and its nearest competitor Chattannooga, Nashville would have 68 out of 100 FORS.

=== 10.8.1 Calculations for Memphis:

10.8.1.1 Memphis vs Nashville

Memphis FOR: 42 Nashville FOR 58 WIN for Nashville

10.8.1.2 Memphis vs Knoxville

Memphis FOR: 42 Knoxville FOR 58 WIN for Knoxville

10.8.1.3 EG Memphis vs Chattanooga

Memphis FOR: 42 Chattanooga FOR 58 WIN for Chattanooga

10.8.1.4 Totals

Memphis FOR: 126

These calculations can be repeated for each pair of choices to set the final ranks. PVS ranks Memphis, with the largest population, as last. FPTP/SVS would rank Memphis first which would be a clear mistake. Imagine that instead of cities, we have various candidates who appeal to different voting blocs. The electorate is better off with the candidate who can represent, be accountable to and relate the best with all the electorate. Imagine that cooperation between people would be related to the geographic distance between cities. The greater the divide the less chance of getting along and in a democracy getting along and making decisions for the majority is important.

10.9 PVS Election- Primaries

PVS pairs off each choice against every other choice. Each pairing results in a WIN, a LOSS, or a TIE. The winning choice would be the one with the most WINS over all other choices based on a direct one on one faceoff.

10.9.1 1st Pair:

Carson VS Cruz

Inputs:

Results:

Carson registers 2 FORS
Cruz registers 3 FORS and 1 WIN

10.9.2 2nd pair:

Carson VS Kashich

Carson registers 3 FORS and 1 WIN
Kasich registers 2 FORS

10.9.3 The Finish:

After Analyzing all the pairs.

Note that Cruz is the clear winner using PVS however using FPTP/SVS he would be dead last with no 1st place votes

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[1] ttps://four-rp-001.web.app/app-dashboard

[2] ttps://en.wikipedia.org/wiki/Condorcet_winner_criterion

[3] ttps://en.wikipedia.org/wiki/First-past-the-post_voting

[4] ttps://en.wikipedia.org/wiki/Instant-runoff_voting

[5] ttps://en.wikipedia.org/wiki/Condorcet_method

[6] [[2]]

[7] ttps://en.wikipedia.org/wiki/2015_Canadian_federal_election

[8] ttps://en.wikipedia.org/wiki/Ranked_pairs

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