[EM] Approval strategy from rankings

[Stephane Rouillon]

MIKE OSSIPOFF wrote :

> (David Gamble I think) continued:
>
> 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.
>
> Sincere rankings:
>
> 50: ABCD
> 50: DCBA
> 50: BCDA
>
> Approval votes inferred as described above:
>
> 50: ABC
> 50: DC
> 50: B

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

> Winners: B & C
>
> Borda scores:
>
> A: 3
> B: 6
> C: 5
>
> B is the unique winner.
>
> It isn't guaranteed to match Borda, because it depends on which 1/3 of the
> voters you have voting for which number of candidates. You can get different
> results by assigning different roles to the different thirds of the voters.
>
Did I misunderstood?

Steph.

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