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Bart Ingles wrote:<br><br>
<blockquote type=cite class=cite cite>The reason I am comparing only the
diagonal (T/T vs. NT/NT) is that the<br>
A and C sides can't know which they are in advance of the election
(in<br>
other words, which is the majority faction). So whatever
strategy<br>
applies to one applies to both; in fact there is no way for the two<br>
sides to distinguish themselves on your matrix in advance of the<br>
election.</blockquote><br>
You're totally missing the point. It doesn't matter whether they
are the stronger or weaker faction. If they turn out to be the
faction with more votes, then truncation does not help them. If
they turn out to be the faction with less votes, truncation ACTIVELY
HURTS them by handing the election to the other side.<br><br>
The only time truncation changes the outcome is when it hurts your
faction (and thereby helps the other faction, which is what is confusing
you).<br><br>
Comparing the top left to the bottom right is, once again, totally
invalid. In my most recent message I showed two matrices. One
applies when CBA has more votes than ABC, and one applies when the
opposite is true. If you want to compare how truncation affects
your outcome in the face of uncertainty, then you need to combine these
two matrices in a probabilistic sense. Here, I'll do it.
before the slash is the result if ABC has more votes than CBA, and vice
versa after the slash.<br><br>
<font face="Terminal, Monaco">xxx| T | NT |<br>
---|-----|-----|<br>
T | A/C | A/B |<br>
---|-----|-----|<br>
NT | B/C | B |<br>
----------------<br><br>
</font>So for the ABC faction, truncation either takes you from B to C,
from A to A, from B to B, or from B to C. None of those are an
improvement. For the CBA faction, truncation either takes you from
B to A, from C to C, from B to A, or from B to B. Again, none of
these are an improvement. There's no need to know the utilities
(other than their ordinal rankings) or the probabilities, since not a
single outcome supports truncation.<br><br>
<blockquote type=cite class=cite cite>In effect, the two sides combine as
a "pool" of votes, and don't know<br>
which side they are on until after the election. In fact by
truncating<br>
they are voting for an AC lottery over a probable B
win.</blockquote><br>
This amounts to voter collusion, and is theoretically possible.
Given the right candidate utilities, this is indeed the prisoner's
dilemma, but as we well know the prisoner's dilemma usually ends with
both criminals picking the Nash equilibrium and ratting out their
pal. In the same way, both factions would have every reason to
betray their collusive rival and vote sincerely once they got into the
voting booth. After all, voting their full preferences could only
help them, just as the truncation of their opposing faction can only help
them.<br><br>
Really, I don't know how many more ways I can say this. This is a
factual, empirically obvious point, and I'm pretty sure you will agree
with me if you just take a step back and work through each individual
possibility yourself. No faction has any logical reason to
truncate. I haven't proven this in a general case, nor have I
checked every possibility, so there is a chance that some obscure
electoral arrangement could provide incentive to truncate (although I
doubt it). But this example is definitely not such a
case.<br><br>
-Adam</html>