Does Quadratic Voting fix Cumulative Voting?

Quadratic voting is a variation of cumulative voting where the cost is not linear with the score.

In regular cumulative voting your score total must add to some cap, say 100. This means in a [0,10] system you could give 10 candidates a 10 since 10*10 =100. Quadratic voting penalizes higher scores in an effort to get people to spread out their votes.

cost = score^2

This means in a [0,10] system you could give only 1 candidate a 10 since 10^2=100. However you can give four candidates a 5 since 5^2+5^2+5^2+5^2=100. This means that people have incentive not to bullet vote.

It has got a lot of fame and even been used in Colorado but I do not see how it is really any better. I am not really that well informed on the issues with cumulative voting. It does not really solve vote splitting so I never considered it viable.

Counterexample

45 A=10
55 B1=7 B2=7

You still have issues of vote splitting. I think this is better for legislative bodies than citizen electorates.

Also, somehow n2 feels a bit harsh; I seem to like 1 + 2 + … + n = n(n+1)/2 better.

I agree. I think the vote splitting is well known. I also agree that the cost function seems arbitrary.

Are there other issues with cumulative voting in general? I suppose it make no claim on any definition of PR.

It’s semi-proportional like SNTV, unless voters get more points than seats, at which point it becomes more majoritarian.

In SNTV, everybody gets one vote since the “S” is for single. In Bloc Plurality (https://electowiki.org/wiki/Bloc_voting) they get the same as the number of winners. Cumulative Voting is when the number of votes is arbitrary.

The number of votes or points each voter is allowed to give can be considered fractions of one vote. Giving a candidate all 10 of your fixed votes is equivalent to giving them one vote in SNTV, if I’m not mistaken.

There’s also the problem of “do you trust voters to do the math right”?

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