[EM] [RangeVoting] A Consensus Seeking Method Based on Range Ballots

[Jobst Heitzig]

Hi friends,

Raph wrote:
> On Sat, Feb 14, 2009 at 7:29 PM,  <fsimmons at pcc.edu> wrote:
>> Note well that in the case of a tie among lotteries the tie is broken by a
>> voter, not the voter's ballot, and the tie breaking voter only decides among
>> the
>> tied lotteries, not directly picking the winner.
> 
> It might be worth collecting 2 ballots from each voter then.  A voter
> could give a strategic ballot and an honest ballot.

To avoid this, the tie-breaking rule could also be this: Amoung those
lotteries in the tie (i.e., those maximizing the product of all ballot
expectations), use the one with the smallest entropy or smallest sum of
ballot variances or something like that.

> This would mean you don't have to find the voter later to ask them to
> pick the winning lottery.
> 
>> Under this ULVM, rational voters in the above scenario will vote
>>
>> 60: [100, 0, 60]
>> 40: [0, 100. 40],
>>
>> which turns out to be the Nash equilibrium with the highest voter
>> expectations.
> 
> Is this true in the general (3 candidate) case, i.e. is the Nash
> equilibrium always for the highest utility candidate to win?

What do you mean by "highest utility"?

> Also, sometimes with Nash equilibria, it can be possible to obtain a
> better result by committing to a stance.  The result of the other
> 'players' adjusting to your solid position can yield higher results
> for you then that Nash equilibrium.

But that would require the other voters to be quite ignorant about your
true utilities, otherwise they would not adjust to your solid position.
This is because then they would know that if they did adjust to your
"solid" position, they would produce a situation which is not a Nash
equilibrium and in which you would have an incentive to deviate from
your claimed "solid" position.

> I wonder if the whole process could be implemented as a DSV method.
> You give your honest utilities and then method casts your vote for you
> based on those utilities.   It then adjusts your vote based on how
> others vote.  The rule would be to find the best Nash equilibrium.

"Best Nash equilibrium" in what sense?

Yours, Jobst