[EM] Unranked-IRV

[Bart Ingles]

Richard Moore wrote:
> 
> 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.

I think that's still considered cumulative voting.  Although
successively eliminating the weakest candidates and recounting the
ballots would not be part of cumulative voting.

I think in most cases it's probably a strategy mistake to give different
weights to your choices in cumulative voting anyway, so this is probably
a good system.  In the rare exceptions, voters can give "statistical"
partial votes simply by tossing a coin or rolling a die to determine
whether to include a candidate.


> 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.

Without elimination it's equivalent to FPP (simply vote for only one
candidate).  With elimination, maybe not.  For all I know the strategy
might be equivalent to approval voting, but the performance of the
system will not be as good (in single-winner elections).  A lot of work
for a worse result.


> 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.

I think you may be mistaken about the optimum strategy for this system. 
My guess is that for some voters, the best strategy will be the same as
FPP, and for others it will be more like approval voting.  This may be a
restatement of the previous paragraph, though -- as when the strategic
value of the candidates are either one or zero.


> > 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?

Yes.  There was even an STV (multi-winner) equivalent.

Bart