[EM] Elections methods performance criterion

[Bart Ingles]

Adam Tarr wrote:
> 
> Ken Johnson wrote:
> 
> >With Borda, the sincere ranking translates to a Borda count identical to
> >the above sincere CR rating,
> >    C1 < C2 < C3 < C4 < C5 < C6  -->  C1(0), C2(1), C3(2), C4(3), C5(4), C6(5)
> >But if you try to use rank equality to mimic CR strategy, it doesn't work
> >quite the same,
> >    C1 = C2 = C3 < C4 = C5 = C6  -->  C1(1), C2(1), C3(1), C4(4), C5(4), C6(4)
> 
> I believe that insofar as Borda allows equal rankings, you would score that
> ballot as
> C1(0), C2(0), C3(0), C4(1), C5(1), C6(1).

I agree with Ken's scoring (1,1,1,4,4,4) for "standard" Borda.  Adam's
scoring (0,0,0,1,1,1) is identical with Donald Saari's proposed
modification, which Saari believes would discourage strategic voting.

I don't think Saari's modification would work.  With that modification
in place, the voter should merely toss a coin.  If heads, the voter can
rank each group of "equal" candidates in ballot order; if tails, in
reverse ballot order.  Assuming other voters do likewise, this strategy
would result in:

1/2 (0, 1, 2, 3, 4, 5)
-plus-
1/2 (2, 1, 0, 5, 4, 3)
-equals-
... (1, 1, 1, 4, 4, 4)
or the same as Ken's scoring.

Note that this effectively makes Borda a "truncated system", which Saari
seems to regard as entirely unsuitable for use in elections.

[KJ]
> >Does this mean Borda is somewhat less susceptible to strategy than CR?

[AT]
> I think I just demonstrated why it is not.  CR strategy never becomes any
> more perverse than "who should I give 100 and who should I give zero?"  In
> Borda, you could have incentive to put your second favorite candidate alone
> in last place.

I agree with Adam on this point.  As far as I can tell, the optimum
strategy with Borda is to try to maximize your favorite's score while
making all other candidates end up with an equal score (so long as their
scores are lower than your favorite's).  If it doesn't look like your
favorite can win, you should pick a "strategic favorite" (i.e. lesser
evil candidate) and maximize his/her score, then rank any favorites
prefered to the lesser evil next, and finally rank the remaining
candidates in whatever way equalizes their scores.

Over all voters, the tendency is probably for all candidates to end up
with the same score, so that the election is ultimately decided by
unpredictable errors in voters' strategy.

Bart