On Sun, 6 Jun 2004, [iso-8859-1] Kevin Venzke wrote:
--- Brian Olson <[EMAIL PROTECTED]> a �crit�:Speaking of "write a new meaning", I challenge that "we all agree" statement. In a recent comment of mine, I claimed that "equal opportunity to vote" is not the same as "equal voting power". You are expressing "equal opportunity to vote" but I think I've seen more usage of 1p1v as "equal voting power".
I read your message but have no idea what you mean by "equal voting power." Can you define it?
"Equal Voting Power"
I think it's a stronger statement of what Arrow calls "the condition of non-dictatorship". In addition to no one voter being able to decide the election, no voter has any more influence in deciding the election than any other.
Approval may not give exactly equal voting power, some voters will choose more or fewer choices, but it at least gives equal opportunity to vote.
Are you saying that a voter has more power if they vote for more candidates?
On second thought I recall the argument that Approval can be considered that a ballot is a YES vote or a NO vote on every choice, and so I guess every voter does actually contribute equally to the process, they just might not contribute optimally for their utility.
Similarly Borda is definitely NOT "one person, one vote".
In the variation where the unranked choices are given the average value of the ranks not used, every voter has equal voting power. ((n(n-1))/2)
If this is true, then equal voting power seems undesirable. If a person truncates then presumably they prefer to give zero points to the truncated candidates.
But then a voter who truncates is given extra power! That power is applied negatively against the choices they truncate. The voter may prefer whatever they want, but I prefer a fair system.
I suppose 'fair' is up for grabs around here, with the various criterion floating around. So, put another way, I want to encourage honest voting. I think in the case of a ranked ballot, I want to encourage a total ranking. Borda with 0-point assignment for truncated choices encourages truncation. Borda with average-unassigned-value assignment encourages a full ranking.
Fascinating historical article. So, it seems to me that the primary objection was that in the second (Nth) round of Bucklin _some_ people might be getting additional votes but not necessarily _all_ people. Someone putting down only a first place choice would be given no additional vote in the 2nd round. I would suggest a distribution like for Borda above. This could be countered by saying that a 1st-only ballot then only casts meaningless votes in Bucklin rounds. I say "equal opportunity to vote", and they didn't take it, they effectively stayed at home past the first round. Dunno if that would hold up in court but I'd love to try. :-)
Does it occur to you that a voter might not *want* to give a vote to a second candidate? It's not as though the first choice is eliminated!
Heh, well, I've never been a Bucklin advocate. Again, I don't like rewarding truncation, which it seems straight Bucklin does. A similar average-unassigned-value variation could fix that. For each round in which the ballot does not specify an Nth place, award the 1 additional vote fractionally between the choices which were not ranked.
Also IRV falls to this logic in the event of an incomplete ballot. If all of an elector's choices that they ranked on their ballot get disqualified, _they get no vote_!
But this would not be fixed by using a "distribution like for Borda above." Could IRV be made to have equal voting power, then?
I don't see how IRV could be fixed to meet "equal voting power", but maybe I'm just not trying. It does pass what I'd call "equal opportunity to vote", where voting with the proper voting strategy (zero info, just how you map your preferences onto the ballot, possibly honestly) gives any voter the maximum voting power. If everyone votes correctly then there is equal voting power. OK, so the fix to IRV is to require total rankings and not allow ties. Just hope you don't have to cast a total ranking on the California Governor Recall (135 candidates).
I claim that a normalized cardinal ratings election satisfies one person equal-power/one-vote.
Why is it important that the method would meet "equal power"?
IMO, "equal power" is fair. With the possible exception that it can wind up being sub-optimal for social utility by giving too much vote to people who don't really care that much, and it puts an unfair cap on people who may be hugely effected by the issue up for vote. But that's really too deep a philosophical problem. "One Person One Vote", "Equal Rights", "equal protection of the laws" are all established ethical expressions that I am comfortable with. So, it seems natural to me that an election method should reflect that equality.
Really, all of these systems that suffer from incomplete-ballot sub-optimality only provide "equal opportunity to vote" and not necessarily "equal voting power". Normalized CR provides both!
What do you mean by "incomplete-ballot sub-optimality"?
I mean that filing an incomplete ballot, an incomplete ranking, is sub-optimal for the expected utility of the voter. A voter is most likely to be the happiest with the outcome by casting a fully ranked ballot. (Or at least, that's the state of affairs I want, see above anti-truncation rants.)
The exception to this could be when there are more choices than a human voter has time to find out about and the voting process becomes "I like this guy --- 1st. And that one a bit less -- 2nd. Ooo, and that one not at all -- Last." and several choices are left unranked. So, how much should an election method penalize this voter for not being fully informed? Little, I hope.
Brian Olson http://bolson.org/
