Rob Lanphier robla at eskimo.com
Tue Dec 31 10:47:37 PST 1996

```This strikes me as a *very* good place to start with a "frequently asked
questions" list.

Perhaps this could be the tool by which we resurrect the ancient
discussion of what belongs on a FAQ (see the archive from last February).

Err, uh, I better stop before someone thinks I'm volunteering for
something :)

Rob

p.s. I don't remember Arrow's being this troubling.  Maybe it's just the
clarity with which you expressed it here, Mike.  Back to the books, I
suppose...

Q:  What is Arrow's Theorom, and why is it significant?
<short explanation of the history of it>

Q:  What were Arrow's four criterion that were considered mutually
exclusive?

On Mon, 30 Dec 1996, Mike Ossipoff wrote:
> Apparently Arrow listed 4 criteria:
>
> Strutural: The input is a finite positive number of rankings
> , from 1st choice to last choice, of a finite positive number
> of alternatives. But only mathematicians would feel that it's
> necessary to include "finite positive...". I must note that
> a real public election is going to have lots of ballots that
> _don't_ list from 1st choice to last choice, but this definition
> that I'm quoting does allow ties, and so everyone you don't rank
> can be considered tied for last in your ranking. The output
> is a single winner (in Bruce's version here, it's a collective
> ranking).
>
> No-Dictator: When there are 3 or more voters & 3 or more
> alternatives, there's no voter who can in principle determine
> the winner every time. (greatly simplified wording)
>
> [These 1st 2 criteria are so obvious that we (you & I) don't
> even regard them as criteria, but obvious starting-point conditions
> that don't even need mentioning. The last 2 criteria are more
> criterion-like]
>
> Independence from Irrelevant Alternatiaves: Removing from the
> election someone who didn't win shouldn't change who wins.
>
> Pareto Criterion: Never elect an alernative that has another
> alternative ranked over it by everyone.
>
> [Pareto sounds like GMC but is much weaker. Every method we've
> discussed meets Pareto, but only 2 (Condorcet & Simpson-Kramer)
> meet GMC]
>
> ***
>
> So those are Arrow's criteria. His impossibililty theorem says
> that those criteria can't all be met.

```