[EM] Satisfaction Approval Voting - A Better Proportional Representation Electoral Method

[Kristofer Munsterhjelm]

Kathy Dopp wrote:

> I believe that may be the case, because a sentence in the paper says:
> 
> "For example, if a
> candidate receives 3 votes from bullet voters, 2 votes from voters who
> approve of two
> candidates, and 5 votes from voters who approve of three candidates, his or her
> satisfaction score is 3(1) + 2(½) + 5(1/3) = 5 2/3."
> 
> and
> 
> "the satisfaction score of subset S, s(S), can be obtained by summing
> the satisfaction
> scores of the individual members of S. Now suppose that s(j) has been
> calculated for all
> candidates j = 1, 2,…, m. Arrange the set of m candidates [m] so that
> the numbers s(j) are
> in descending order. Then the first k candidates in the rearranged
> sequence are a subset
> of candidates that maximizes total voter satisfaction."
> 
> and
> 
> "Because candidates c and d are the two candidates with the highest
> satisfaction scores,
> they are the winners under SAV."
> --------
> 
> What are its flaws that you see?
> 

I'll consider it in greater detail when I have more time, but plain SNTV 
has two problems.
The first is the "ordering of the vote" problem, which means that in 
order to achieve proportionality, voters have to spread their votes 
equally among party candidates. Parties in Taiwan use rather ingenious 
strategies (like telling a voter to vote for a candidate depending on 
the voter's birthday) to ensure this.
This shouldn't be a problem for the cumulative vote version - each voter 
just votes for all the party candidates so that the mechanism 
distributes the vote fairly.

The second is that voters have to take into account how popular the 
candidate is; too much, and the vote is wasted (because the candidate 
would win anyway), too little, and the vote is wasted (because the 
candidate won't win).
This, however, might be. It's like Approval strategy, but more complex: 
if the voter votes for a candidate that wouldn't win anyway, he weakens 
his other votes and so helps the other candidates less. Similarly, if 
the voter votes for a candidate that has already passed the threshold, 
that candidate can't "win more", and so that vote, too, is wasted. 
Knowing the expected relative support of each candidate becomes very 
important in such a system.

Now, you may say that the second problem is analogous to STV's Woodall 
vote management (don't vote for a candidate that would otherwise win), 
but the problem is not as serious in STV because STV has a contingency 
mechanism; if you vote for a candidate that still loses, for instance, 
your vote may have some chance of being transferred to one of the 
choices where your vote makes a difference.
To not give the wrong impression, I'll say that the property here (that 
your vote counts towards those that could be elected) is more important 
than the specific method (in this case STV). My Webster-based monotone 
setwise method achieves something similar by having a vote count toward 
all sets of candidates ranked higher than or equal to the candidate in 
question, and the outcome is then constrained to have the same 
proportion of members from each set as voters that supported that set.