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Bart Ingles wrote:<br><br>
<blockquote type=cite class=cite cite>Adam Tarr wrote:<br>
> Specifically, there is the remarkable fact that a voter in a
winning<br>
> votes-based Condorcet voting system can NEVER be hurt by fully
expressing<br>
> their preferences. There are cases where fully voting your
preferences can<br>
> fail to help you, but it can never actually hurt you.<br><br>
Never is a strong word. </blockquote><br>
True, and I lack a rigorous proof, but every empirical example I have
seen supports this. Your example is no different...<br><br>
<blockquote type=cite class=cite cite> How about the
following:<br><br>
(projected vote percentages shown; assumed accurate to within +/- 5<br>
percentage points)<br><br>
45% A B C<br>
5% B A C<br>
5% B C A<br>
45% C B A</blockquote><br>
There's no sense in talking about uncertainty and ties; it only confuses
the issue. Let's just assume one or the other camp has more votes,
and see if in that light, either side has an incentive to truncate.
If neither side has such an incentive, then neither side has that
incentive in the toss-up case as well (since they know they either have
more votes or less votes than the other guy). Without loss of
generality, I'll give A the edge, which gives us:<br><br>
46 ABC<br>
5 BAC<br>
5 BCA<br>
44 CBA<br><br>
Pairwise votes are:<br><br>
B 56 > C 44<br>
B 54 > A 46<br>
A 51 > C 49<br><br>
In this case, B is the Condorcet winner.<br><br>
If both sides truncate we get<br><br>
46 A<br>
5 BAC<br>
5 BCA<br>
44 C<br><br>
Pairwise votes are:<br><br>
A 51 > C 49<br>
A 46 > B 10<br>
C 44 > B 10<br><br>
Now A wins the election in either winning votes or margins (don't stop
the presses yet).<br><br>
Now, if only the A camp truncates:<br><br>
46 A<br>
5 BAC<br>
5 BCA<br>
44 CBA<br><br>
Pairwise votes are:<br><br>
B 54 > A 46<br>
A 51 > C 49<br>
C 44 > B 10<br><br>
B wins the election in winning votes, and C wins the election in
margins.<br><br>
Finally, if only the C camp truncates:<br><br>
46 ABC<br>
5 BAC<br>
5 BCA<br>
44 C<br><br>
Pairwise votes are:<br><br>
B 56 > C 44<br>
A 51 > C 49<br>
A 46 > B 10<br><br>
A wins the election in winning votes or in margins.<br><br>
OK, let's look at the decision matrix. Here is the pairwise matrix
of decisions for each camp, and the candidate elected, for each
method:<br><br>
(I apologize in advance if the tables look lousy. Try cutting and
pasting into a text editor with uniform character spacing if it looks
bad. I used the "terminal" font type if that
helps.)<br><br>
The top row is the tactics of the ABC faction, the left column is the
tactics of the CBA faction. T = truncate, NT = do not
truncate.<br><br>
Margins methods:<br><br>
<font face="Terminal, Monaco"> | T | NT |<br>
---|---|----|<br>
T | A | A |<br>
---|---|----|<br>
NT | C | B |<br>
-------------<br><br>
</font>Winning Votes methods:<br><br>
<font face="Terminal, Monaco"> | T | NT |<br>
---|---|----|<br>
T | A | A |<br>
---|---|----|<br>
NT | B | B |<br>
-------------<br><br>
</font>OK, so what can we conclude from this? If the CBA voters
truncate, they always get A elected in either system. This is a
"strictly dominated strategy" to use the game theory
name. There's no way the B voters should truncate,
regardless.<br><br>
In winning votes methods, truncation for the ABC voters makes no
difference (i.e. does not hurt them, even if it fails to help
them). In margins methods, truncating can prove costly for an ABC
voter. This is neither here nor there for the purposes of my
analysis; I can show you a counter-example where truncation can help in
margins cases.<br><br>
The point is, nowhere here do we get any suggestion that a voter in a
winning votes method can be helped by truncation. My initial
contention still stands.<br><br>
<blockquote type=cite class=cite cite> But then I don't see
truncation as necessarily a bad thing. If truncation can defeat a
"hated middle" candidate, it addresses my main misgiving about
the Condorcet methods.</blockquote><br>
Much in the same way that we can't differentiate between the indifferent
voter and the lazy voter, we cannot distinguish between the
"respected (if unglamorous) compromise middle" and the
"hated (yet still) compromise middle". Smart CBA voters
in an approval election will still approve B, to defeat A, anyway.
What method would actually prevent B from winning when the voters act in
a logical manner? Even plurality and IRV encourage CBA voters to
dump C for B if they have perfect information.<br><br>
-Adam</html>