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 <[email protected]> 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
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