[EM] Simulating multiwinner goodness

[Brian Olson]

On Mar 11, 2010, at 11:29 AM, Jonathan Lundell wrote:

> As with any choice system based on cardinal utility, there end up being two problems that are not, I think, amenable to solution. One is the incomparability of individual utility measures from voter to voter (and here we're talking about utility deltas, since the utilities are normalized to max=1.0). The other is that, even if comparability were solved, we don't have a means of, in the individual case, determining what they are.

Arrow made the same mistake. We can't compare interpersonal utility, but in practice we do. We set everyone's utility to One. One person one vote. That's how much you get.

> In particular, reported utility isn't very useful, since for the system to work, we need sincere utility, and a utility-based system provides every incentive to strategize. And, as Terry suggests, it's not clear what we *mean* by utility here. Happiness with what? The outcome of the individual election? The makeup of the resulting legislature? The legislation resulting from that legislature?

Reported utility is vulnerable to all kinds of noise, imperfect reporting, imperfect introspection, and so on. And yet this can be simulated. We can make sim people who are perfectly knowable, add that noise, run the election, and see what happens both compared to the noisy utility and true utility. When I did this it turns out there are some methods less vulnerable to noise! (Condorcet better, IRV, with it's non-monotonic threshold swing regions is more vulnerable to noise.)

> And even if we could somehow measure the voter's ultimate happiness as a function of legislative outcome and come back in time and cast a vote, we don't have utilities for the counterfactual alternatives.
> 
> However attractive it might be to fantasize about functions from cardinal utility to social choice, it comes down to an attempt to square a circle or invent a perpetual motion machine. The attemp might be fun, but we know a priori that it will fail.

Are we talking about real people or sim people? I think we can make simulations and models that are useful. Lots of people keep trying, including me. Or are you sayng that we can't reasonably make sim people whose knowable sim qualities bear any useful resemblance to the real world? We're talking about all kinds of mathematical properties of election methods, why not various measures under stochastic test? What would be a good measure?