[EM] Arrow's theorem and cardinal voting systems

[Kristofer Munsterhjelm]

On 10/01/2020 05.46, robert bristow-johnson wrote:

> my question that i have asked the Score Voting or Approval Voting
> advocates years ago remains: "How much should I score my second choice?"
> or "Should I approve my second choice or not?"  that tactical question
> faces the voter in a Score or Approval election the second he/she steps
> into the voting booth.  but not so for the ordinal Ranked ballot.

I tended to phrase this as: Approval requires that the voters engage in
manual DSV (or earlier, that they "dither" - in the sense of reducing a
full-color image to black-and-white). Approval satisfies so many
properties on paper by placing the burden on the voter instead.

But I've recently found a paper that puts this very clearly:
https://www.jstor.org/stable/1955800 (use Sci-Hub if you don't have
access). The paper shows that if the voter preferences aren't naturally
dichotomous (a bunch of equal ranked candidates at top above a bunch of
equal ranked candidates at bottom), then the Condorcet winner may end up
being dead last by approval score; and that for a particular type of
strategy, any candidate may be an equilibrium Approval winner.

To quote from the conclusion: "Strategic calculations are endemic to AV
even though all of the votes considered are called sincere. Given the
literature's emphasis on approval and disapproval sets - even the name,
approval - and the fact that voting for all approved candidates and no
others is optimal for dichotomous preferences, one gets the false
impression that AV will eliminate strategic thinking and voting. The
results here show that this is far from true, however."