Talk:Lottery paradox

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Preface instead of Smullyan

Smullyan's paradox as stated here is really a variant of the preface paradox rather than the lottery paradox. I would suggest deleting the Smullyan section and replacing it with a more explicit connection to the Preface. — Preceding unsigned comment added by Catrincm (talk • contribs) 17:47, 15 September 2016 (UTC)[reply]

This is entirely correct; the Smullyan variation is the preface paradox, not the lottery paradox. I've deleted the section. Mwphil (talk) 16:09, 16 November 2022 (UTC)[reply]

Question

I'm not really seeing the paradox at all either. Is this just a question of how the 'AND' operator operates on probabilities?

As an example, lets say that the probability of something being "very likely true" is when : P_A > X, that is the probability of A being true being greater than a probability X.

So the statement would read, "if it rational to believe (P_A > X) and rational to believe (P_A' > X), then its rational to believe (P_A > X) & (P_A' > X).

So the result of the statement is based on the & operator. If, according to probability theory, P_A and P_A' are statistically independent (it should be noted they are not statistically independent in the lottery case) the operator would of course reduce to, P_A*P_B > X. At that point you just show the statement can be false by choosing appropriate values of X and P. Did they not have a standard definition of the & operator on probability when the paradox was prevalent?Gsonnenf (talk) —Preceding undated comment added 03:01, 8 April 2009 (UTC).[reply]

Paradox?

This just seems like a problem caused by rounding error and not necessarily a paradox. —Preceding unsigned comment added by Jvclark2 (talk • contribs) 02:24, 1 October 2008 (UTC)[reply]

Proposed rewrite

Hi. I've offered a proposed rewrite of this article, following the structure of Gregory Wheeler "A Review of the Lottery Paradox", in Harper and Wheeler (eds.), Essays in Honour of Henry E. Kyburg, Jr., 2007.

Expansion & clean up

Hi all. I think this article really needs some expansion and clean up, such as:

Info on different formulations of the paradox (e.g., John Hawthorne (2004) and others formulate it as a puzzle about knowledge, not just justification).
A section on proposed solutions to the paradox.
The relation to contextualism.

These are just a few suggestions. - Jaymay 21:38, 17 August 2006 (UTC)[reply]

Types of lotteries

This also assumes a lottery in which only tickets sold have a chance of winning -- e.g. unsold tickets cannot be drawn. This seems to be the standard where you buy a ticket and fill out the stub, the latter being drawn at the end of the contest. This paradox would not apply to lotteries where serial-numbered tickets are sold and a random number generator of some sort picks the number (like the old Olympic Lottery back in the '70s). "You could win a million, just by spending ten...you may never be this close again!" --SigPig 11:37, 21 July 2006 (UTC)[reply]

Keep in mind that the puzzle is meant to only be concerned with certain types of lotteries or lottery-type situations. (I added a note in the article trying to mention that.) John Hawthorne (2004), following others, even shows how the puzzle extends to non-lottery situations. So the puzzle is not about anything that falls under the word "lottery". It concerns specific types of probabilistic situations involving knowledge attributions and claims of justification. Such situations just happen to be largely lottery-like and the introduction of the puzzle in the liturature was primarily in the context of lottery situations (because they easily bring out the more general puzzle/paradox). - Jaymay 21:38, 17 August 2006 (UTC)[reply]

Conjunction vs Closure Principle

The article says that three principles are inconsistent. The first two are correct but the third states:

If it is rational to accept a proposition A and it is rational to accept another proposition A', then it is rational to accept A & A'

This is what is sometimes called 'the conjunction principle' not to be confused with the closure principle which states that:

If it we are justified in accepting A and A entails B, then we are justified in accepting B. It is the first two principles plus closure which yeild the paradox. The first two plus the conjunction principle won't do it. —Preceding unsigned comment added by 86.15.10.59 (talk) 20:21, 13 March 2009 (UTC)[reply]

Another related point is that, the article claims that the probabilists traditionally reject 1) and with it, the basic probabilistic acceptance rule. In actual fact, the orthodox response from formal epistemologists etc. has been to reject closure. Indeed the guy who came up with the paradox (name escapes me) didn't consider it a paradox but an argument clearly demonstrating the failure of the closure principle. 86.15.10.59 (talk) 20:26, 13 March 2009 (UTC)[reply]

Update citation style?

Any objections to moving this article to the <ref>...</ref> citation style to match most of the other articles in this category? — xaosflux ^Talk 17:33, 15 September 2014 (UTC)[reply]

Not from me. Paradoctor (talk) 18:56, 15 September 2014 (UTC)[reply]

5thfloorlattimore, any comment from you a significant referencer would be welcome as well. Thank you, — xaosflux ^Talk 01:26, 16 September 2014 (UTC)[reply]

This seems more like an issue of language or understanding than a paradox.

The proposition is that there is a 1000 ticket lottery that has exactly one winner.

It is safe to assume that any one ticket won't win, because the chances are 1/1000. But it's not safe to assume that no ticket will win because it's stated that there is exactly one winner. If you assume that tickets 1, 2, 3, and so on until 1000, any ticket i (i between 1 and 1000 inclusive) will not win, you would be incorrect because you're assuming about multiple tickets even though the only statement made safe to assume is that any ONE ticket won't win.

68.132.4.4 (talk) 01:33, 25 April 2018 (UTC)RJ[reply]

Other lottery paradoxes

Pardon my uncouth interruption, but what other lottery paradoxes are there? A lottery buyer faces a dilemma: if she sticks to minimum purchases, she stays away from the law of large numbers (by which she is destined to lose in favour of the lottery owner) and truly takes her chances. On the other hand, each extra ticket bought adds to her chances of winning. Does the theory of probability have a clear advice for lottery buyers, then? (I guess the opposing points may converge considering that average buyers follow the same attraction in buying more tickets and therefore keeping the chance of a win by the average buyer constant). --ilgiz (talk) 01:35, 26 October 2018 (UTC)[reply]