On Feb 24, 2007, at 11:36 , Michael Ossipoff wrote:
I'll start with order-reversal, because that's what Juho's example was
about:
Order-Reversal:
In the example below, the A voters prefer B to C, but are using
offensive
order-reversal in order to take victory from B. The B voters could be
regarded as not having a preference among A and C, or considering A
to not
deserve a vote, or they could be defensively truncating (but with
margins it
won't work, and they need more drastic misrepresentation of their
preferences in order to save B):
101: AC
100 B
50: CB
The B & C majority prevent A from winning by merely not ranking A.
This is
an SDSC example. And it's a margins SDSC failure example.
I'll comment these examples from the point of view of real large
scale public elections (since that is the #1 target use case).
I see two extremists, A and C, and one centrist, B.
The fact that all B voters truncate (in sincere votes) would probably
not happen in real life. But even if some of them would vote BA and
some BC the scenario would still work.
One weakness in the scenario is that A supporters need lots of
strategic voters to make their plan work. With these numbers they
need all the 101 voters. 100 strategic voters means a tie, and 99 or
less voters means that the strategy will not work. (The rest will
vote sincerely AB.) Making all voters of a country follow the
strategy is more or less an impossible task. Maybe you can find
numbers that make the strategy more credible in real elections.
Another weakness is that when others will hear of the strategy plan
that will change the way other voters will vote. (In large public
elections the strategy can not be kept secret.) If three of the B
voters decide to vote BC (sincerely since they don't like the tactics
of A), the strategy will not work. (Two voters => tie.) I believe
this amount of change in the opinions is quite possible and even
quite probable.
Note also that if B voters vote BC as described above the winner is
C. That is the worst result from A supporters' point of view. The
strategy thus has a major risk of leading to a worse result than the
original result (compromise candidate B). (Note that also small
differences between the poll results that were used when planning the
strategy and the actual election day opinions may have the same effect.)
One more possible problem is that the method should work well also if
the votes that you listed above were sincere votes. But the margins
results of the candidates are so close to each others that I will not
comment :-).
In summary I'd say that in real elections the probability that this
strategy would work is approximately 0 (at least with these numbers).
And the risk of donating the victory to C by voting AC is too high
for the A supporters.
Truncation:
Either the A voters prefer B to C, but are employing offensive
truncation
(successfully in margins), or they don't have a preference among B
and C, or
maybe they're just being lazy, or are in a hurry. If they prefer B
to C,
then B is the CW, just as in the previous example:
101: A
50: BA
100: CB
Again, A wins in margins. The offensive truncation succeeds. Or,
maybe lazy
or hurried truncation took victory from B. Truncation doesn't
affect wv in
this way. With no one falsifying a preference, the B & C majority
can keep A
from winning merely by voting sincerely. This is an SFC example.
And it's a
margins SFC failure example.
There were two different sincere opinion alternatives for the A
supporters: AB or A.
In the second case the votes listed above are sincere and we are back
to comparing the choices that margins and winning votes make. And
again the margins results are so close to each others that (when
trying to defend the margins viewpoint) I can't comment :-).
Let's discuss more about the case where the sincere opinion of the A
supporters is AB.
It looks like A and B supporters are close to each others since their
second sincere preferences are B and A respectively. C supporters are
not related but for some reason they like B more than A.
Let's check again how many strategic votes the A supporters need. The
result is the same as above, 100 for a tie and 99 or less for the
strategy to fail. And again, making almost all supporters of A vote
according to the planned strategy is more or less impossible in large
public elections.
Let's check also what could happen when other voters hear of the
strategic plan. B supporters may feel betrayed. Let's say that three
of them will vote B instead of BA. The strategic plan fails (as in
the first example). And again, the winner is then C, the worst
alternative from A supporters' point of view. There is thus also a
major risk in applying the strategy.
I'd say the A supporters would be much better off if they would not
try this strategy. The strategy seems to almost certainly fail and
the probability of electing C increases if the number of A supporters
following the strategy is high.
Summary. At least with these numbers the two strategies don't seem to
work in practical large scale public elections. Winning votes seemed
less vulnerable to these attacks than margins but that property is
not needed unless the strategies are a real threat.
Juho
Mike Ossipoff
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