[EM] Arrow's Theorem.

[Rob Speer]

On Mon, Jul 14, 2003 at 01:17:05PM -0500, Adam Haas Tarr wrote:
> Wow, Eric went to the source and got the answer.  Good work.
> 
> So, Arrow's original approach to the theorem could be summed up like this:
> 
> 1) monotonicity + IIA => Pareto Efficiency.
> 
> 2) IIA + Pareto Efficiency => Dictatorship

Hold on. Isn't "preferential ballots" an essential ingredient to the
theorem?

I believe that Approval satisfies non-dictatorship (duh), Pareto
optimality (if you get 100% of the vote, then of course you win), and
IIA (adding a new candidate doesn't change the approval totals for
existing candidates).

I'm also fairly sure it's monotonic; the only changes you can make are
to change a NO vote to YES (giving the candidate one more approval
point) or changing a YES vote to NO (giving the candidate one less
approval point).

Craig Carey seems to think otherwise, but his example doesn't make any
sense. It seems to be replacing a set of preferences with a different
set of preferences that we are supposed to accept as being equivalent.
Why I'm supposed to accept that is not clear, and the reason probably
lies in the mass of unreadable broken English. Craig, seriously, get
someone to help you write in English.

Not that I think Approval is great; my biggest objection to it is that
people don't know how many candidates to vote for, and changing the
wording of the voting instructions could cause huge shifts in the
totals. But the fact remains that it seems to be immune to Arrow's
theorem because it is not preferential.

-- 
Rob Speer