Hello James,
Thanks for the comments.
On Jul 27, 2005, at 14:07, James Green-Armytage wrote:
Hi Juho,
Glad that you're still thinking about this fascinating issue (voter
strategy in Condorcet methods).
You have constructed an example in which margins is less vulnerable
than
WV. However, I suggest that it is just as easy (if not more so) to
construct an example in which the reverse is true.
I think the correct way forward would be to write those examples down
and then see what we have and estimate then relative vulnerability (of
winning votes, margins and pair-wise methods in general) to strategies.
In my opinion, the key
difference is that when strategy does become a concern, WV allows for
more
stable preventative counterstrategies than does margins.
I think the main battle should be fought already before the
counterstrategies will be applied. I mean that normal voters would
probably be unable to understand and apply counterstrategies and having
to deal with them would give a bad impression of the voting method. I
tend to think that if people would need to stop voting sincerely and
start using strategies and counterstrategies, it could be better to
forget that voting method and use some simpler method instead (IRV?,
approval?, two round runoff?). I'm however living in the hope that
pair-wise comparison methods would in most cases be strategy free
enough so that voters could trust the method and vote sincerely
(without being afraid that the few remaining strategic voters (there
will be some in any case) could get their way through).
Not that WV is
necessarily always stable, but that its instabilities are less severe
than
margins when they occur.
The pairwise comparisons in your example are B>C>A. The B>C defeat
has a
bigger margin than the C>A defeat, but a smaller WV count. A reverse
example can be constructed by flipping these two relationships, i.e.
making it so the defeat against the potential "strategizer" has a
bigger
WV count but a smaller margin than the defeat from the strategizer.
I'll use a similar scenario. The Democratic candidate is A, the more
moderate Republican is B, and the less moderate Republican is C.
30 AB
18 AC
11 B
16 BC
25 CB
One difference between the examples is that in my example Democrats
left Republicans unranked while in your example Democrats always rank
Republicans and Republicans themselves don't express opinion on "C vs.
A". The former looks more probable in real life. Or maybe there are
cases where also the latter type of partial ranking is common(?). Do
you have some "real life explanation" why people voted like they did?
Pairwise comparisons
B>A 52-48
A>C 48-41
C>B 53-47
This example is not immediately vulnerable using a WV method, but it
is
immediately vulnerable using a margins method, in that the A voters can
win by burying B.
In my opinion, this incursion is more severe than the one in your
example, because that changed the winner to a fairly similar candidate
to
the sincere winner, whereas in this example the new winner is evidently
quite different.
In your example winner was changed from a Republican to a Democrat.
That is quite severe (I had however above some doubts about if this set
of votes is probable in real life elections). A is on the other hand
the most popular candidate (48% of the votes), almost as strong as the
two Republicans together. In my example the new winner (C) was disliked
by both republicans and democrats. That's also severe.
I should also calculate how easy/difficult it is to apply the different
strategies (number of votes needed, risks etc.) but that's too much for
now and I leave that for further study.
Also, it is somewhat reassuring that BA voters (assuming
that some B voters are BA) can prevent incursion in my example using
WV by
truncating, whereas they would have to order reverse in margins to get
the
same effect.
This is something that I don't think will happen in real life, and
something I don't want to happen in real life. I'd be very happy if
real life elections could be held without requiring voters to apply
complex counterstrategies.
A bit more about risk-reward ratio in your WV example. Yes, there is
not
much risk of the C voters' strategy leading directly to the election
of A,
if it is clear that A is a Condorcet loser. However, if word of the C
voters' strategy gets out to the B voters, and causes alienation
between
the two factions which leads to mutual truncation, A does win. Assuming
that B and C are fairly similar, this means that the risk-reward ratio
may
actually be fairly high.
As already noted I don't like counterstrategies (in real life
elections). I however think the anger of the B voters is justified. B
voters however don't win anything if they manage to make A the winner
(unless one considers revenge as one type of victory :-). The game
appears quite tricky if both B and C voters apply strategies and
counterstrategies and try t react each others' anticipated voting
behaviour.
I'll give these examples some more thoughts also after these initial
comments. Producing stable conclusions may take time though.
For me one interesting point in this discussion is the fact that
different strategy examples exist. If they are reasonably similar in
all directions, I have some interest in favouring margins since I find
it to be a more natural measure than winning votes is. I don't however
want to jump to conclusions. I just note that various strategic
problems exist and I hope they are not too serious to make Condorcet
methods unusable in general. Rather than recommending use of strategies
and counterstrategies I hope that strategies are unusable enough to
allow people to vote sincerely. Maybe lack of exact information on how
people are going to vote and dislike of strategic voting and voters
will do the job.
Thanks again for the counterexample. I hope we get a good collection of
them and good analysis of the associated risks and probabilities.
BR, Juho
my best,
James Green-Armytage
http://fc.antioch.edu/~james_green-armytage/voting.htm
20 A
15 ABC
10 ACB
35 BC
20 CB
- Democrats have nominated candidate A.
- Republicans have nominated two candidates. In addition to their
normal mainstream candidate B they have nominated also a right wing
candidate C.
- All voters have taken position on Democrats vs. Republicans.
- Some Democrat voters have not taken position on the Republican
internal battle between B and C.
- All Republican voters have taken position on B vs. C.
- Democrats prefer B over C.
- Republicans prefer B over C.
- B is the Condorcet winner.
- In raking based real life elections it seems to be quite common that
voters don't give full rankings. This example has only three
candidates
and therefore full rankings could be quite common. But the election
could have also considerably more than three candidates, in which case
partial rankings probably would be quite common. It is probable that
ranking candidates of competing party is less common than ranking
candidates of ones own party (just like in this example).
Now, what if some of the the 20 C supporters (C>B voters) would note
the weak position of C before the election and decide to vote
strategically C>A>B.
- in the case of winning votes C wins the election with 6 to 20
strategic votes (out of the 20 C>B votes)
=> quite efficient and risk free (if one has reliable opinion poll
results available) (and if others don't use other strategies)
- in the case of margins A wins the election with 11 to 20 strategic
votes (out of the 20 C>B votes)
=> not very promising as a strategy
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