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diff --git a/blog/voting.org b/blog/voting.org new file mode 100644 index 0000000..eff2ec0 --- /dev/null +++ b/blog/voting.org @@ -0,0 +1,38 @@ +#+title: Representative Voting +#+author: Preston Pan +#+description: What do we do about voter turnout? Voting demographics? Polarization? +#+html_head: <link rel="stylesheet" type="text/css" href="../style.css" /> +#+html_head: <link rel="apple-touch-icon" sizes="180x180" href="/apple-touch-icon.png"> +#+html_head: <link rel="icon" type="image/png" sizes="32x32" href="/favicon-32x32.png"> +#+html_head: <link rel="icon" type="image/png" sizes="16x16" href="/favicon-16x16.png"> +#+html_head: <link rel="manifest" href="/site.webmanifest"> +#+html_head: <link rel="mask-icon" href="/safari-pinned-tab.svg" color="#5bbad5"> +#+html_head: <meta name="msapplication-TileColor" content="#da532c"> +#+html_head: <meta name="theme-color" content="#ffffff"> +#+html_head: <meta name="viewport" content="width=1000; user-scalable=0;" /> +#+language: en +#+OPTIONS: broken-links:t +* Introduction +Current voting systems are broken, and people argue about ways to solve it. Many talk about about ranked-choice +voting or other ballot-systems, but I argue that the real problem in voting has to do with game theory principles. +In this article I endorse a system that has been tried out before, but has been forgotten: /random representation/. I +argue that it has game theoretic foundations that make it superior to other kinds of voting systems. + +** The Model +Let us assume that there is a small probability that you can swing the election $$ \rho $$, and a cost to voting; that +is to say, it takes some amount of time, which has opportunity cost associated with it to vote, which we +will call $$ \alpha $$. Let us assume that there is a high /reward/ in swinging the vote; that is to say, if you were +the one that swings the vote, your vote is worth some high monetary value. Let $$ \beta $$ be the median price of swinging. +Let $$ n $$ be the number of people voting, and let the weight of each vote be equal between all participants. +Let the choice of candidate between all voters be binary; voting for one candidate mutually excludes you from +voting for another, and there are two candidates (this is to simply the model; you will see that this does not +lose generality). Then, let us model the expected value of voting for singular individuals. + +For a given person, the probability that your vote swings (or at least ties) depends on the probability that +$$ x = \frac{n - 1}{2} $$, where $ x $$ is the number of people that vote for your candidate. The probability +density function for the probability that $$ m $$ people vote for your candidate we'll call $$ f $$. We will assume +it is binomial, and you might expect it to be closer to 50/50 most of the time, but that is pretty hard to model. +We will therefore compensate by modeling it more accurately afterwards. For now, we assume all participants have +a 50% chance to pick either candidate. +\begin{align*} +\end{align*} |