[EM] Two simple alternative voting methods that are fairer than IRV/STV and lack most IRV/STV flaws

[Brian Olson]

On Jan 13, 2010, at 8:06 PM, Kathy Dopp wrote:
> 1. A rank choice ballot method:
> 
> Any number of candidates may be running for office and any number
> allowed to be ranked on the ballot.
> 
> Voter ranks one candidate vote =1
> 
> Voter ranks two candidates, denominator is 1+2 = 3
> votes are worth 2/3 and 1/3 for first and second ranked candidates
> 
> Voter ranks three candidates, denominator is 1+2+3=6
> votes are worth 3/6 and 2/6 and 1/6 for 1st, 2nd, and 3rd choice respectively
> 
> Voter ranks four candidates, denominator is 1+2+3+4=10
> votes are worth 4/10, 3/10, 2/10, and 1/10 for 1st, 2nd, and 3rd and
> 4th choice respectively
> 
> ETC. Just follow the same pattern

This sounds like a variation on Borda count, but with an incentive to vote on fewer candidates. With smaller and smaller votes as I give more information, I should vote for one _maybe_ two choices. Why would I want to give my favorite a 4/10 vote when I could give them a 2/3 vote or a 1.0 vote? This is the wrong incentive. Giving more information on the ballot should be encouraged.

> 2. A point system where a total number of points per voter per contest
> may be allocated by the voter to any of the candidates running for
> office:
> 
> Two candidates running for office, give all voters 2+1=3 votes to
> cast.  They may cast all three votes for one candidate or split the
> votes any way between the two.
> 
> Three candidates running for office, give all voters 3+2+1=6 votes to
> cast. They may cast all six votes for one candidate or split the votes
> any way they like between the three.
> 
> Four candidates running for office, give all voters 4+3+2+1=10 votes
> to cast. They may cast all ten votes for one candidate or split the
> votes any way they like between the four.
> 
> Five candidates running for office, give all voters 5+4+3+2+1=15 votes
> to cast. They may cast all 15 votes for one candidate or split the
> votes any way they like.

This is equivalent to any other normalized ratings ballot. People vote ratings, but they all have the same voting power, either by straight sum of ratings or by geometric distance or something.
In any system where the voter has to allocate the points themselves, there will be nasty strategic thinking going on to try and allocate the points best.
If I vote simply and honestly, allocating points in alignment with how I feel about candidates, points not in differential between the top two candidates are wasted.

Kathy, in my investigations of election methods, I started with straight rating summation as optimal, but normalized ratings as more fair, but then ran into the wasted-vote problem and settled on "Instant Runoff Normalized Ratings" ( http://bolson.org/voting/methods.html#IRNR ). Over the course of rounds of counting it reallocates your vote based on your original ballot to always be optimally applied to the choices available. Never mind the "Instant Runoff" part of the name, by using ratings ballots and considering the whole ballot at once, it's much better than the simplistic IRV. It's much less non-monotonic than IRV, and gets better answers in my simulations.

You can compare the relative non-monotonic areas in these election space plots:
http://bolson.org/voting/sim_one_seat/www/

http://bolson.org/voting/sim_one_seat/www/4a_IRV.png
http://bolson.org/voting/sim_one_seat/www/4a_IRNR.png
http://bolson.org/voting/sim_one_seat/www/4a_Condorcet.png