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