Morosoph's Journal: Arrow's Theorem on Voting

Arrow's Theorem came up in a recent discussion where I commented on the virtues of Single Transferable Vote. It seems to me that the axiom of the Independence of Irrelevent Alternatives is in fact too strong: to me it makes a difference as to the degree of intent where I rank different candidates in an election, and what the degree of separation is. If I rank candidates fifteenth and twentieth, I probably want my vote to have at least as much influence in differentiating the two than if they were fifteenth and sixteenth, but not less. The candidates between the two do matter, particularly if one of them drains my "residual vote", and this axiom is used throughout the proof.

This bothers me, because this theorem is a real show-stopper for those who'd want to reform the electoral system, and the way people are, if you can't show that a new system is perfect, they settle for an inferior state of affairs which is the status quo.

My question is this: is there a better alternate axiom or set of axioms that can reasonably distinguish voting systems, so that we can meaningfuly say that one is in some way superior to another?

Since writing the above, I discovered ElectionMethods.org, which is worth a look. At present, I favour Condorcet, then Single Transferable Vote (here's why). Anyone have any better ideas?

As this Journal entry's been archived, anyone who wants to comment will need to post here, on the unofficial Bruno forum.

Footnote (6th June 2007) : There's an interesting note on Arrow's Theorem at condorcet.org.