<div dir="ltr"><div><div>Dear Bayle,<br><br></div>your proposed square-root solution violates the principle of "one person, one vote, one value", as votes have different weights.<br><br>A better solution to the Mafia problem in proxy voting is to have public voting but secret voters and proxies.<br>
</div><div>This solution has the positive side-effect of focusing the debate on issues and not on people.<br></div><div><br></div>Best regards<br>Peter Zborník<br><div><div><div><div><br>Dne pondělí, 8. dubna 2013, Bayle Shanks <<a href="mailto:bshanks3@gmail.com" target="_blank">bshanks3@gmail.com</a>> napsal(a):<br>
><br>> Typically when large numbers of people are voting you'd like to have<br>
> secret ballots so that the Mafia can't buy votes or intimidate people<br>> and also so that people feel free to make unpopular choices.<br>><br>> However, when the people voting are representing others, you often<br>
> want to publish who voted for what so that the constituents can use<br>> the past voting records of their representatives to decide whether to<br>> vote for them in future elections.<br>><br>> In a proxy voting system, where voters can allow other voters to vote<br>
> for them 'by proxy', and particularly in a transitive proxy voting<br>> system, where the proxies can be re-proxied (e.g. Alice can give a<br>> proxy to Bob who can give both Alice's proxy and his own to Caroline),<br>
> you want to satisfy both these objectives.<br>><br>> You want everyone's vote to be secret, because you don't want the<br>> Mafia to intimidate them or buy their votes, and you want unpopular<br>> outcomes to be feasible.<br>
><br>> But you also want everyone's votes to be<br>> public, because you don't want to give your proxy to someone who says<br>> they'll do one thing with your proxy and then actually does another,<br>
> without you ever knowing.<br>><br>> One fear is that the Mafia will say, 'You'd better give me your proxy<br>> or you'll be punished'. I think you can probably fix that by not<br>> giving proxy holders very precise information on how many proxies they<br>
> hold, when they were given, or who gave them.<br>><br>> Even if each person casts their own vote secretly, but can see which<br>> way their own proxied vote was vast, the Mafia just has to<br>> secretly ally with a small number of proxy givers in order to see<br>
> which way the proxied votes are being cast (note that even if the<br>> system let the vote caster know whose proxies they hold, they<br>> don't know which proxy-ers are allied with the mafia).<br>><br>> One idea is just to say, if you accept proxies your votes are<br>
> public, otherwise they are secret. This essentially reduces the<br>> transitive proxy system to ordinary voting however because<br>> it provides no way to have proxy holders who can cast proxied votes in<br>> a way that the Mafia can't control.<br>
><br>> Here's an idea I had to deal with this problem.<br>><br>> Give each person two ballots: a secret ballot and a public ballot.<br>><br>> Everyone can see which way they vote their public ballot. If they hold<br>
> proxies from others, the proxies' secret ballots follow their secret<br>> ballot and the proxies' public ballots follow their public ballot. The<br>> originators of the proxies don't ever find out which way their secret<br>
> ballots were cast.<br>><br>> To tally the vote, for each candidate, you sum the secret ballots for<br>> that candidate, then you sum the public ballots for that candidate,<br>> then you multiply these two sums together, then you take the square<br>
> root.<br>><br>> After transforming sums in this manner, you can use most existing<br>> voting methods to determine the winner.<br>><br>> For instance, if there are five voters and two candidates, and they<br>
> vote like this:<br>><br>> PUBLIC BALLOT<br>> CANDIDATE<br>> VOTER A B<br>> 1 1 0<br>> 2 1 0<br>> 3 1 0<br>> 4 0 1<br>> 5 0 1<br>
><br>> SECRET BALLOT<br>> CANDIDATE<br>> VOTER A B<br>> 1 1 0<br>> 2 0 1<br>> 3 0 1<br>> 4 0 1<br>> 5 0 1<br>><br>
> then the public ballot tally for A is 3, the secret ballot tally for A<br>> is 1, the public ballot tally for B is 2, the secret ballot tally for<br>> B is 4; the combined tally for A is sqrt(3 + 1) = 2, the combined<br>
> tally for B is sqrt(2 + 4) = 2.45.<br>><br>><br>> Virtues:<br>> * you can use your secret ballot to express your true preference<br>> * however, if you care about influencing the election, you can have<br>
> the most impact if your secret ballot matches your public ballot. So<br>> there is at least some incentive not to lie about what you plan to do<br>> if you accumulate proxies.<br>><br>> I expect that what would happen is that the Mafia would<br>
> be limited to corrupting public ballots (and people lying about what<br>> they are doing with their proxies to attract proxies from the<br>> opposition party would be limited to corrupting secret<br>> proxied ballots). If the Mafia can only reach a subpopulation of<br>
> voters, then that subpopulation will effectively have less weight,<br>> because the multiplication of the public and the secret tallies<br>> effectively downweights voters who cast their public and secret<br>> ballots differently.<br>
><br>> A slightly different approach would be to provide only public ballots,<br>> but in addition a way for each person to secretly submit a request to<br>> ignore their public ballot while counting votes. So now the Mafia can<br>
> effectively prevent you from voting but they can't do anything more.<br>> You'd have to find a way to implement this so that the Mafia can't use<br>> the same information that allows the vote-counters to match ballots to<br>
> ignore requests to find out how you voted, however.<br>><br>> Thoughts? Other solutions?<br>><br>> thanks,<br>> bayle<br>><br>> ----<br>> Election-Methods mailing list - see <a href="http://electorama.com/em" target="_blank">http://electorama.com/em</a> for list info<br>
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