[EM] The matter of whether people strategize
Bill Lewis Clark
wclark at xoom.org
Mon Jan 19 12:39:03 PST 2004
Bill Lewis Clark wrote:
> Furthermore, I'd like to point out that even if a sizable majority of
> the voting population *were* to vote strategically, their strategy would
> necessarily take into consideration the effects of those voters who
> *don't* vote strategically. In particular, the ratio of strategic to
> non-strategic voters is itself a major point of consideration, in
> devising a voting strategy.
MIKE OSSIPOFF replied:
> You keep saying that, but have never justifed your claims. How would
> you incorporate the ratio of strategic to non-strategic voting in your
> Approval strategy? I assume that you have an Approval strategy like
> that, because you wouldn't just be blowing hot air, would you?
I'm sometimes wrong, but I never blow hot air :)
I worked out an example using Cardinal Ratings / Range Voting, which also
works the same if you switch to Approval -- given certain assumptions
(which I'll get to in another email.)
Assume the following sincere voter preferences for candidates ABCD:
(Group I) A:10 B:1 C:2 D:0 46%
(Group II) A:1 B:9 C:10 D:0 28%
(Group III) A:0 B:2 C:1 D:10 26%
If everybody voted sincerely, the election results would be:
A 4.88
B 3.5
C 3.98
D 2.6
Now assume everybody voted strategically as follows:
(Group I) A:10 B:0 C:10 D:0 46%
(Group II) A:0 B:10 C:10 D:0 28%
(Group III) A:0 B:10 C:0 D:10 26%
(Group I must support C in order to block Group II&III support of B, which
they use to prevent A from winning. The Group I second-choice candidate B
is the best they can hope for in this situation. Group II is happy
because their first choice wins. Group III has no option except to
continue supporting B, lest their least-favorite candidate A win. So,
nobody is willing to switch their support, and these strategies end up
being optimal.)
Results:
A 4.6
B 5.4
C 7.4
D 2.6
Now assume half vote strategically, and half vote sincerely. First, we'll
simply combine the ratings from the previous two scenarios:
(Group Ia) A:10 B:1 C:2 D:0 23%
(Group IIa) A:1 B:9 C:10 D:0 14%
(Group IIIa) A:0 B:2 C:1 D:10 13%
(Group Ib) A:10 B:0 C:10 D:0 23%
(Group IIb) A:0 B:10 C:10 D:0 14%
(Group IIIb) A:0 B:10 C:0 D:10 13%
However, the bottom half of this data no longer represents the optimal
strategies. The combined support for B from the strategic voters in
Groups IIb&IIIb is no longer enough to challenge A's victory, so the
strategic voters in Group Ib have no reason to support C.
So, the actual situation would be something like this:
(Group Ia) A:10 B:1 C:2 D:0 23%
(Group IIa) A:1 B:9 C:10 D:0 14%
(Group IIIa) A:0 B:2 C:1 D:10 13%
(Group Ib) A:10 B:0 C:0 D:0 23%
(Group IIb) A:0 B:10 C:10 D:0 14%
(Group IIIb) A:0 B:10 C:10 D:10 13%
And the results:
A 4.74
B 4.45
C 4.69
D 2.6
(There is some leeway in how Groups IIb&IIIb may vote -- but the key point
is that Group Ib definitely has a different optimal strategy, depending on
what percentage of the voters vote strategically.)
Mike, you acknowledged this point in a later post entitled "Info doesn't
change extreme voting in CR" so I'm sure this particular example isn't
really a surprise to you -- but you did challenge me to back up my
assertions, so there you go. (I'll back up the rest shortly.)
I'll get back to my main claim -- that the optimal strategies for AV and
CR/RV will differ, assuming a significant percentage of the voters are
sincere -- in my next email.
-Bill Clark
--
Dennis Kucinich for President in 2004
http://www.kucinich.us/
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