[EM] Consensus?: IRV vs. Primary w/Runoff

[Forest Simmons]

On Wed, 30 Jan 2002, Steve Barney wrote in part:

> Forest:
> 
> Let me try to clarify what I meant in the previous message. First, here is a
> definition.
> 
> Primary w/Runoff:
> Elected candidate shall receive 50% plus one or more of the votes cast. If more
> than two people are nominated, a run-off shall occur between the two people who
> receive the most votes in the first round of voting if in that round one person
> does not receive 50% plus one or more of the votes cast.
> 
> Now, here’s my argument:
> 
> If there are 3 candidates with the same voters, and the voters’ preferences
> remain static between the first and second ballot, the two procedures are
> mathematically identical, and will yield the same result.
> 
> If there are 4 or more candidates, the Instant Runoff voting procedure is less
> manipulatable than the Plurality with a Runoff voting procedure, due to the
> fact that voters cannot purposefully change their order of preference from one
> balloting to the next. 

I don't follow how being unable to make later adjustments makes the
whole game less manipulable.

It seems to me that if there is a possibility for later adjustments I can
ignore those who are trying to manipulate me before the first move by
taking a "wait and see" stance. 

Those who want to manipulate before they have to make irreversible moves
can bluff freely about their intentions.  After they have made their first
move, at least that much becomes a matter of public record. Every move
they make decreases their potential for manipulation. The more moves they
make before your final move, the better informed it will be.


> 
> Given the same voters and the same sincere preferences, the only mathematical
> difference between these two procedures is that the IRV is less manipulatable
> than the Primary w/Runoff procedure. 
> 
> Therefore, IRV is better than the common Primary w/Runoff voting procedure in
> the sense that it is either equally or less likely to violate any given
> mathematically described fairness criteria, such as manipulability.

How do you mathematically define "manipulability?"  Perhaps we could test
your definition against your claim that IRV is less manipulable than two
step runoff.


> 
> The reason I say “mathematically described” fairness criteria, is that I
> want to exclude the political questions for the sake of the argument.
> For example, some might argue that repeated balloting is better because
> the voters may be more informed in a subsequent balloting, and can
> change their preferences according to that new information. I consider
> that to be a political question, and I wish to leave that debate to
> others. 

It seems to me that any definition of manipulability, mathematical or not,
would have to take into account potential reactions to information
(accurate or not), since no manipulation can take place in a zero
information environment.

All seriously proposed election methods are subject to manipulation,
because all require strategy to one degree or another to maximize expected
outcome, and all optimal strategies require information about the
intentions of the other players.

The more sensitive the optimal strategy is to the other players
intentions, the more manipulable the game. When some of the strategy can
be based on perfect information about past moves instead of relying
entirely on imperfect estimates of intentions, then some of the
manipulability is removed. 


> Furthermore, that particular claim seems to muddle the
> manipulation issue to the point where it becomes impossible to prove
> (mathematically) one way or another. You have to hold certain things
> constant to make the manipulation argument. 

It would be nice if you could be more specific about what needs to be held
constant.

I think that comparing a simulation of one method with another method of
which it is not a simulation is an example of NOT holding something
constant.

We have two methods and their simulations (instant methods), giving a
total of four methods to compare.

In my first posting in this thread I explained why the two step runoff is
strategically equivalent to its simulation. [Quick recap, all of the
manipulation has to be done before the first move, because the second move
is a final non-manipulable head-to-head contest for the winner.]

So far we have stayed constant on the number of steps, while passing from
non-instant to instant version of the runoff.

Now let's compare the two instant versions (IRV with the two step
simulation). In other words, this time the constant is the level of
reality (both are mere simulations): As Bart pointed out, the potential
for manipulation increases as the number of steps increases, since in the
two step method all ranking after the first rank is not subject to
manipulation, whereas in IRV all ranks are subject to manipulation. 

Now we see the following chain. IRV is more manipulable than the two step
simulation, which is strategically equivalent to actual two step runoff.

Therefore, IRV is more manipulable than two step runoff.

Forest