[EM] Unranked-IRV

[Richard Moore]

MIKE OSSIPOFF wrote:

> >I would like to share perhaps the simplest majority-empowered reform over
> >our current election problems.
> >
> >I'll call this system: Unranked-IRV. It works like IRV but doesn't allow
> >voters to rank preferences, only list them like approval, however unlike
> >approval votes are divided so each voter only gets one total vote among all
> >choices.
>
> When you give the voter a fixed amount of vote, and let him divide
> it among the candidates, that's "single-winner Cumulative", a method
> that's known to be strategically equivalent to Plurality--one should
> give one's whole vote supply to the candidate for whom one would vote
> if it were a Plurality election.

Cumulative voting allows the voter to give different-sized votes to each
candidate, providing that the total of all his votes is less than or equal
to some constant. What Tom is proposing, I think, is that the voter has
a single vote that may be divided equally among the candidates he likes.
So if you want to approve 3 candidates, A gets 1/3, B gets 1/3, and C
gets 1/3.

Although I'm not satisified that this is the case, it's possible that this
constraint may keep the voter from giving all his vote to one candidate.
The strategy would have to be evaluated in the context of an elimination
procedure, so it's not obvious to me whether this is the case.

I've been thinking of another alternative to cumulative, in which the voter
gives his ratings for each candidate. The voter's ratings are then scaled
by an amount which is equal to the square root of the sum of the squares
of his or her ratings. I don't know if this method has been discussed
before, but I call it Normalized Ratings.

In Normalized Ratings, the voter's optimum strategy is to vote for each
candidate a rating that is proportional to the voter's strategic value for
that candidate. Thus, it avoids the drawback of Single-Winner
Cumulative, but it obviously fails to elicit a sincere vote, so it leaves a
lot to be desired. However, while an equally-divided approval vote
might encourage single-candidate voting in a non-eliminating counting
procedure, when combined with an elimination procedure it just might
avoid both the problem of Single-Winner Cumulative and the
problem of Normalized Ratings.

> When the lowest votegetter is eliminated your vote fraction on him
> is divided among the others for whom you've voted?
>
> It might very well be as good as IRV with equal rankings and
> divisible one vote, or maybe better, and so it might meet WDSC,
> but almost surely will violate FBC & SFC.

It sounds to me like it is exactly "IRV with equal rankings and
divisible one vote", if I interpret that phrase (and Tom's proposal)
correctly. So maybe Tom's method has been discussed on this list
before. Has it?

 -- Richard