[EM] Remember Toby

[Juho Laatu]

On 29.5.2011, at 1.33, Kevin Venzke wrote:

> Margins elects A here:
> 35 A>B
> 25 B
> 40 C
> 
> Is this going to be defensible when this method is proposed? Can you
> argue a case for A without mindreading off of the blank areas of the 
> ballots?

I guess the common assumption is that the unranked candidates are considered to be tied at the last position. So, vote "B" should be read "B>A=C".

(The intended meaning of "B" and "B>A=C" is thus the same by default. Some methods may however have an implicit "approval" cutoff at the end of the explicitly ranked candidates. In that case vote "B" should be interpreted "B | A=C" and "B>A=C" should be interpreted "B>A=C |", but I consider that to be a special case. If the voter has some preference between A and C (and she wants to express it), then the voter should mark that in the ballot, since otherwise there is no other sensible interpretation but that A and C should be treated as equal. If there are so many potential winners in the election that one can not expect all voters to rank all potential winners, then we may lose some of the information that the voters wanted to give. I'm not sure if I answered properly to the mindreading point here but those were my thoughts anyway.)

Why would margins elect A then? The explanation is simple from the margins point of view. If we elect A then there are 40 voters saying that C should have been elected instead of A and 5 less saying than A is better. If we elect B then there are 35 voters saying that A should have been elected instead of A and 10 less saying than B is better. If we elect C then there are 60 voters saying that B should have been elected instead of C and 20 less saying than C is better. From that point of view A is the least controversial winner. A would need only 6 additional votes to become a Condorcet winner and beat all others.

> the voters give you a single majority decision (more than half the
> voters) and that's the one you don't respect?

That could happen in margins. It is possible that the winner is opposed by a majority of the voters, and in all other pairwise comparisons the winning side has less than majority of the votes, but those comparisons are stronger when measured as difference between winning and losing side (e.g. 30: A>B, 21:B, 49: C). I'm not sure when majorities should be given precedence and what majorities that would mean. In large elections there is seldom a majority of all the people or the whole electorate. In the case of margins above in all the pairwise comparisons the winning side had majority of all the voters that wanted to express their opinion in that pairwise contest (although not a majority of all the valid ballots of that election).

Juho