[EM] river, ROACC
jarmyta at antioch-college.edu
Fri Aug 27 06:07:32 PDT 2004
>Just to repeat myself [another time ;-] : We must consider
>NON-DETERMINISTIC methods like ROACC (see my post on the
Okay, I will consider them! : )
I do greatly appreciate your ability to write serious new voting methods,
and I absolutely do not want to ignore them. Sometimes it takes a bit of
time for a new method or a new idea to soak in, but I want to keep working
I am only just now beginning to appreciate the river method. I didn't see
the justification for the rule before, but I was recently impressed to
learn that it passes independence of pareto-dominated alternatives. Yes, I
know that was discussed months ago, but I'm a little slow on the uptake
sometimes. By the way, for anyone who missed it, I'd like to call
attention to this post by Jobst which seems to catalogue every possible
kind of four candidate cycle... quite an impressive bit of work,
On to probabilistic methods now...
First, I agree with you that ROACC is simple. Very simple, very easy to
explain, and yes, it can be performed in the comfort of your own home.
Second, I do agree with you that strategy in pairwise methods is worth
doing something about. I have engaged in lengthy discussion on this point.
However, you will hopefully understand my reservations about using a
probabilistic method for public elections... I just feel uncomfortable
using random selection to make such an important choice as the selection
of a president, etc. I suspect that the general public will feel the same
way. Basically, I think that resolving cycles randomly is a too-drastic
way of addressing strategy concerns. If there is a sincere cycle, I think
that a random resolution is quite unsatisfactory.
Instead, I request that you evaluate my weighted pairwise method. I
believe that this will substantially reduce the strategic instability of
pairwise, and will also provide a more meaningful resolution to sincere
cycles than strictly ordinal methods.
The current version of the proposal is at
With regard to sincere cycles, I think that it provides a very sensible
definition of which defeats are the weakest, i.e., the least significant
to voters. With regard to strategic manipulation forming insincere cycles,
this method makes it so that those who have the most desire to change the
sincere result have the least ability to do so, and those who could
conceivably alter the result through duplicity are those who are
relatively sympathetic to the original winner to begin with. In the same
way, it means that the candidate elected by a strategically altered result
should not be too radically different from the sincere winner, i.e.,
shouldn't be his polar opposite or arch-enemy. Fully ordinal pairwise
methods can make no such promise.
Oh, and by the way, I still think that there can be strategic incentive
in ROACC. Imagine these sincere preferences
40: Bush > Kerry > Nader
15: Kerry > Bush > Nader
30: Kerry > Nader > Bush
15: Nader > Kerry > Bush
Let's imagine further that for the Bush > Kerry > Nader voters, the
respective utilities of those candidates are Bush 100 > Kerry 10 > Nader
Note that Kerry beats Bush by 60-40 and Nader by 85-15. Let's imagine
that the Bush voters have read the polls and see the chances of Kerry
winning to be around 90%, and the chances of Bush winning to be around
10%. So, you could calculate the probabilistic utility of the election for
them, via (.9 x 10) + (.1 x 100) = 19.
However, what if they were to vote Bush > Nader > Kerry instead, causing
a cycle? Then there would be a 33% chance of each candidate winning. The
new probabilistic utility of the election would be (.33 x 100) + (.33 x
10) + (.33 + 0) = 36.7. That's a gain, so the strategy is rational.
Of course, if the Nader voters become widely aware of the strategy, then
they have the option of preventing it from working by voting Nader = Kerry
> Bush. But then again, maybe some of them will be interested in the 33%
chance of Nader winning the election. Tempting...
So the sincere Condorcet winner will not necessarily survive even if the
voters are rational.
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