# [EM] Re: river, ROACC

Jobst Heitzig heitzig-j at web.de
Sun Aug 29 09:16:05 PDT 2004

```Dear James!

> 	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
> 0.
> 	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.

You would be right if I was to admit that there is anything like a
"utility function" -- which I do not: I believe that it is absolutely
misleading to think the utility of an option could be measured in any
way. If it could, people would always have complete preference orders,
which they don't. There are definitively situations in which none of two
options is "better" than the other, and even if that were the case, you
would at most get a utility function on an ordinal scale, that is, a
ranking. I firmly believe that the best information you can get or
assume about the pairwise preferences of a person is the information
whether A or B is considered better, A and B are considered equally
good, or none of the three (resulting in an arbitrary binary relation,
but that is another ongoing discussion :-) !

However, assuming there was something like utilities, I still don't
think the above example is as severe a problem as others for two
reasons: First of all, as you realized also, there is a
counter-strategy. Secondly, it is quite improbable that any Bush voter
will reverse his/her Kerry/Nader preference as you suggest, because that
will result in his worst option (Nader) with quite a large probability
(1/3). Do you really think voters will take that risk? I don't.

Summarizing:
1. There is no such thing as a real valued utility function.
2. A counter-strategy is a good deterrent.
3. The risk of getting a worse outcome is an even better deterrent.
4. Both together are the best deterrent you could have :-)

All the best, Jobst

```