[EM] Majority winner set

[Bart Ingles]

Dear Markus:

You wrote:
> 
> Of course, it is possible that a given voter makes strategical considerations
> and gets to the conclusion that voting _sincerely_ is the best _strategy_.
> But nevertheless it makes sense to differ between sincere voters and
> insincere voters. When a given voter makes strategical considerations and
> gets to the conclusion that he cannot get any advantage by voting insincerely,
> then this is a desirable situation. When a given voter makes strategical
> considerations and gets to the conclusion that it is advantageous to vote
> insincerely, then this is not a desirable situation.

To me there are degrees of undesirability, depending on the type of
strategy used and on the effects of that strategy:

1)  I consider it worse if voters actually reverse preferences, than to
either express a preference where there is none or abstain where there
is a preference.

2)  I consider it worse if the insincere strategy worsens the outcome. 
It is still undesirable if insincere strategy tends to improve the
outcome, but less so -- this just means that strategy provides a means
to compensate for a system's shortcomings.  It's perhaps undesirable
that this is necessary, but it's better than not compensating for the
shortcomings.

3)  I consider it worse if the needed strategy is overly obscure or
complex, or misleading in the sense that some voters are fooled into
using it incorrectly or lulled into falsely thinking it unnecessary

Depending on the above, insincere strategy can be more important or less
important than other concerns -- do you agree?  If not, it seems to me
that the only option is the raffle method, where each voter chooses a
single name, and one of these ballots is selected randomly (which does
this violate -- non-dictatorship, or non-imposition?)


> In other words: It is not a problem that a given voter makes strategical
> considerations after he has got additional information about the voting
> behaviour of the other voters. But it is a problem when this given
> voter changes his own voting behaviour because of these strategical
> considerations.

But if there weren't a chance of this happening, there would be no
strategical consideration.


> I suggest the following definition of sincere voting in Approval Voting:
> 
>    A voter votes "sincerely" when he approves all those candidates
>    he prefers to the incumbent and disapproves all those candidates
>    to which he prefers the incumbent.

It might work where the incumbent is the obvious front-runner -- at
least it gives the voter the flexibility of whether or not to vote for
the incumbent -- but there are situations where it wouldn't make sense:

1) There is no incumbent, or
2) The incumbent has no particular advantage over one or more other
candidates.