[EM] Strategic Range Voting: An Example

[James J Faran]

I thought this example might be of some interest.  I'm not certain of
its import. I'll give the example first and append my comments.

Range Voting with range 0-10; seven alternatives A, B, C, D, E, F, G;
100 voters. Sincere (whatever that means) ratings are given in the table
below, whose last line gives the total point score for the alternatives.

 #    A   B   C   D   E   F   G
24   10   9   3   2   1   0   0
22    9  10   0   1   2   3   0
14    2   1  10   0   0   0   3
14    1   2   0  10   0   0   3
13    1   2   0   0  10   0   3
13    2   1   0   0   0  10   3
TOT 519 517 212 210 198 196 162

So we now assume that every voter knows this information prior to the
actual vote and that everyone decides to vote strategically. They all
see that A and B have more than twice the vote of anyone else, and think
(fools) that its a race between A and B, so everyone maximizes the
difference in their ratings of A and B without changing their preference
ordering. The resulting vote:

 #    A   B   C   D   E   F   G
24   10   0   0   0   0   0   0
22    0  10   0   0   0   0   0
14   10   0  10   0   0   0  10
14    0  10   0  10   0   0  10
13    0  10   0   0  10   0  10
13   10   0   0   0   0  10  10
TOT 510 490 140 140 130 130 540

The result: The candidate with the lowest sincere score gets elected!

Commentary:

This is not a realistic scenario: the ratings of 24 people of 7
alternatives will not be all identical, the use of strategic voting by
all concerned is unusual, the availability of sincere totals is hard to
explain.

The lowest ranked being elected after strategic voting does not look to
be a frequent occurrence. In particular, I'm not certain I could come up
with an example with fewer than seven alternatives. It's certainly
doesn't seem to be as obvious a problem as Warren Smith's DH3 scenario.

There shouldn't be any complaint about the strategic result. A majority
liked G better than either A or B. 

Note that Condorcet methods -- I haven't checked them all -- give the
sincere win to A or have A and B tied. Borda count goes to A. However, a
small change (have the first 46 voters change their rating of G from 0
to 1, and yes, 46% of the voters changing may not be a small change) and
G is a Condorcet winner (now sincerely ranked fifth).

The real strategic idiots are the voters who like A and B best. If they
just kept their high rankings of each other, A or B would still win.
Only, how high should they rank their second choice? Too much, and their
second choice wins over their first choice, and they need the other guys
to rate their second choice higher or their last choice (G) wins. This
is starting to sound very much like the awful game that gets played with
some strategic Borda voting.

Note that the last 54 voters could lock in G by bullet voting G (well,
and their favorite). Indeed, G is a possible winner, but not if you look
at the sincere tallies. If everyone considers the set of possible
winners to be {A,B,G}, the strategic vote changes.

Thanks for reading this far. Your comments welcome.

Jim Faran