[EM] secret ballots and proxy voting

[Peter Zbornik]

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 <bshanks3 at 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
>
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