Comments on: Arrow’s Impossibility Theorem and The Voting Paradox http://mindyourdecisions.com/blog/2008/02/12/game-theory-tuesdays-someone-is-going-to-be-unhappy-an-illustration-of-the-voting-paradox/ Articles on game theory and personal finance Thu, 09 Feb 2012 18:20:00 +0000 hourly 1 http://wordpress.org/?v=3.3.1 By: Maria http://mindyourdecisions.com/blog/2008/02/12/game-theory-tuesdays-someone-is-going-to-be-unhappy-an-illustration-of-the-voting-paradox/comment-page-1/#comment-13067 Maria Sat, 10 Dec 2011 05:41:42 +0000 http://mindyourdecisions.com/blog/2008/02/12/game-theory-tuesdays-someone-is-going-to-be-unhappy-an-illustration-of-the-voting-paradox/#comment-13067 Thank you so much for simplifying Impossibility theorem. Thank you so much for simplifying Impossibility theorem.

]]> By: Applying game theory to relationships, MBA, parenting – 4 videos by Barry Nalebuff - Mind Your Decisions http://mindyourdecisions.com/blog/2008/02/12/game-theory-tuesdays-someone-is-going-to-be-unhappy-an-illustration-of-the-voting-paradox/comment-page-1/#comment-6634 Applying game theory to relationships, MBA, parenting – 4 videos by Barry Nalebuff - Mind Your Decisions Wed, 26 May 2010 09:02:21 +0000 http://mindyourdecisions.com/blog/2008/02/12/game-theory-tuesdays-someone-is-going-to-be-unhappy-an-illustration-of-the-voting-paradox/#comment-6634 [...] A voting paradox [...] [...] A voting paradox [...]

]]> By: AMMJ Wijesiriwardene http://mindyourdecisions.com/blog/2008/02/12/game-theory-tuesdays-someone-is-going-to-be-unhappy-an-illustration-of-the-voting-paradox/comment-page-1/#comment-6387 AMMJ Wijesiriwardene Sat, 13 Mar 2010 17:16:11 +0000 http://mindyourdecisions.com/blog/2008/02/12/game-theory-tuesdays-someone-is-going-to-be-unhappy-an-illustration-of-the-voting-paradox/#comment-6387 I was reading 'Nontransitive Paradoxes' by Martin Gardner. It explains a little bit of Arrow's Impossibility theorem & voting paradox, which i couldn't understand properly. So I was looking for a better explanation over the web and came across this article. After reading all the explanations and ideas I could get a broader view of the problem. I suppose this type of explanations are the best for complicated problems. Thank you I was reading ‘Nontransitive Paradoxes’ by Martin Gardner. It explains a little bit of Arrow’s Impossibility theorem & voting paradox, which i couldn’t understand properly. So I was looking for a better explanation over the web and came across this article. After reading all the explanations and ideas I could get a broader view of the problem. I suppose this type of explanations are the best for complicated problems. Thank you

]]> By: Other Wise » Casual Nash http://mindyourdecisions.com/blog/2008/02/12/game-theory-tuesdays-someone-is-going-to-be-unhappy-an-illustration-of-the-voting-paradox/comment-page-1/#comment-2479 Other Wise » Casual Nash Fri, 29 Aug 2008 01:46:26 +0000 http://mindyourdecisions.com/blog/2008/02/12/game-theory-tuesdays-someone-is-going-to-be-unhappy-an-illustration-of-the-voting-paradox/#comment-2479 [...] to thoroughly understanding any auction or voting system) and Pareto Efficiency in another article, Arrow’s Impossibility Theorem and The Voting Paradox. Good [...] [...] to thoroughly understanding any auction or voting system) and Pareto Efficiency in another article, Arrow’s Impossibility Theorem and The Voting Paradox. Good [...]

]]> By: Presh Talwalkar http://mindyourdecisions.com/blog/2008/02/12/game-theory-tuesdays-someone-is-going-to-be-unhappy-an-illustration-of-the-voting-paradox/comment-page-1/#comment-914 Presh Talwalkar Fri, 15 Feb 2008 00:37:28 +0000 http://mindyourdecisions.com/blog/2008/02/12/game-theory-tuesdays-someone-is-going-to-be-unhappy-an-illustration-of-the-voting-paradox/#comment-914 @Joon: That's an excellent question if your vote really matters. It's actually a very complicated problem, and I don't know the answer, but here's one game theory model. A vote is considered "pivotal" if it breaks a tie. Pivotal votes are really the ones that matter in determining how a state goes. I think having a pivotal vote is less frequent the larger the state--the more voters, the more dispersion in outcomes (51/49, 52/48, etc.). The smaller you are, the easier it is to have a 50/50 split. I think this is the logic of swing states: these are pretty big states, but the votes are nearly 50/50, so it's more likely your vote is pivotal, and hence voter turnout should be larger. On the other hand, it's a circular type of game. If too many voters are discouraged in a large state, then only a few voters will turn out and those will be more likely to be pivotal... All said and done, it might not be worth it to think if your vote really "counts" since it's too complicated to figure out. It's probably better to just vote for other reasons: civic duty, feeling good, or representing your community. @Joon: That’s an excellent question if your vote really matters. It’s actually a very complicated problem, and I don’t know the answer, but here’s one game theory model.

A vote is considered “pivotal” if it breaks a tie. Pivotal votes are really the ones that matter in determining how a state goes.

I think having a pivotal vote is less frequent the larger the state–the more voters, the more dispersion in outcomes (51/49, 52/48, etc.). The smaller you are, the easier it is to have a 50/50 split.

I think this is the logic of swing states: these are pretty big states, but the votes are nearly 50/50, so it’s more likely your vote is pivotal, and hence voter turnout should be larger.

On the other hand, it’s a circular type of game. If too many voters are discouraged in a large state, then only a few voters will turn out and those will be more likely to be pivotal…

All said and done, it might not be worth it to think if your vote really “counts” since it’s too complicated to figure out. It’s probably better to just vote for other reasons: civic duty, feeling good, or representing your community.

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