[EM] Approval strategy from rankings

[Bart Ingles]

Bart Ingles wrote:
> The main reason is that, while we have no information about the voters'
> utilities for each candidate, the voters themselves surely would.
> 
MIKE OSSIPOFF wrote:
> They don't. That's the assumption. All I said was that, if a voter doesn't
> have opinions about rating the candidate, but only has a ranking of the
> candidates, then that voter should vote for the best half of the candidates.

[BI]
That was your assumption, and given that interpretation, I don't dispute
your results.  But that wasn't the only possible interpretation, given
the data.  I thought it more reasonable to assume that the voters had
utilities (& therefore approval cutoffs), but that they weren't shown in
the rankings.

[MO]
> Sure, I'd try to rate them, but in an one actual decision situation, I
> preferred to just rank the alternatives by each consideration and use Borda,
> instead of CR. I knew the merit order of the alternatives by each
> consideration, but didn't want to try to guess ratings. Voters could have a
> similar feeling about candidates.

One small point, I was assuming that the voters had definite utility
levels, not that they necessarily would have wanted to rate the
candidates.  Since the exercise was to derive approval ballots from
rankings, I used utility distribution as a way to generate the rankings.

The fact that you preferred to use Borda rankings in a given situation
could also be interpreted as a utility-based decision, i.e. giving the
candidates equidistant ratings.  If you had felt that some alternatives
were very good, and the rest very bad, you might have used a different
approach.


[BI]
> Thus in a four-way race, for a block of voters with identical preference
> orders, I would assume that 1/3 approve of three candidates, 1/3 approve
> two candidates, and the final 1/3 bullet vote. I believe this would give
> results identical to Borda.
> 
[MO]
> Sincere rankings:
> 
> 50: ABCD
> 50: DCBA
> 50: BCDA
> 
> Approval votes inferred as described above:
> 
> 50: ABC
> 50: DC
> 50: B
> 
> Winners: B & C

[BI]
Stephane had my meaning:

[SR]
I disagree. Approval votes inferred as described above: 
50/3: ABC 
50/3: AB 
50/3: A 
50/3: DCB 
50/3: DC 
50/3: D 
50/3: BCD 
50/3: BC 
50/3: B 
Approval winner: B

Borda scores (x50/3): 
A: 3 
B: 6 
C: 5 
D: 4 
Borda winner: B 

[BI]
The approach that has each voter approving exactly two candidates would
yield:

A: 50
B: 100
C: 100
D: 50