The principles that rule this blog

Principles that will govern my thoughts as I express them here (from my opening statement):


  • Freedom of the individual should be as total as possible, limited only by the fact that nobody should be free to cause physical injury to another, or to deprive another person of his freedoms.
  • Government is necessary primarily to provide those services that private enterprise won't, or won't at a price that people can afford.
  • No person has a right to have his own beliefs on religious, moral, political, or other controversial issues imposed on others who do not share those beliefs.

I believe that Abraham Lincoln expressed it very well:

“The legitimate object of government is to do for a community of people whatever they need to have done, but cannot do, at all, or cannot
so well do, for themselves — in their separate, individual capacities.”


Comments will be invited, and I will attempt to reply to any comments that are offered in a serious and non-abusive manner. However, I will not tolerate abusive or profane language (my reasoning is that this is my blog, and so I can control it; I wouldn't interfere with your using such language on your own!)

If anyone finds an opinion that I express to be contrary to my principles, they are welcome to point this out. I hope that I can make a rational case for my comments. Because, in fact, one label I'll happily accept is rationalist.

Monday, March 10, 2008

And now for a digression...

Taking a bit of a break from the 2008 election, I've just discovered a fascinating site. I've never been very happy with the way we vote here, using plurality or "first-past-the-post" voting, but most of the proposals I've seen for reform leave me cold. In particular, I'm rather hostile to the "approval voting" system, where you vote for all the candidates you can support, but with no way to distinguish between someone you really don't like and someone you're unfamiliar with. Now I've found just the system that fills the bill; it's called "range voting." You can rate each candidate, something like the way we rate books or CDs on Amazon, and the highest total rating wins. See the site here.

22 comments:

BROKEN LADDER said...

actually approval voting is the simplest form of range voting, and has almost the same social utility efficiency, measured in bayesian regret.

http://rangevoting.org/UniqBest.html
http://rangevoting.org/BayRegDum.html

so approval voting does yield excellent results, even if it makes you feel less able to express yoself.

it would be a good solution for range voting advocates who cannot convince the public/government that the larger ballot and more complex counting of a 0-10 ratings system is worth it. approval voting has the upper hand in that case, because of its incredible simplicity. you just take away the 1-candidate maximum in our current system and let people vote for as many candidates as they want. it would be vastly better than our current system and other pseudo-solutions like instant runoff voting.

http://rangevoting.org/Approval.html

Opinionator said...

Thanks for your comment. But I've never liked the "all or nothing" aspect of approval voting. In the recent contest for the GOP nomination, I would certainly have cast a vote for McCain and Giuliani if approval voting had been used, and not for Huckabee, Brownback, and the like. But what of Romney? I'd want to give him a chance to win against a Huckabee, but not to help him against Giuliani or McCain. In a 1-10 range vote, I could have given, say, 9 or 10 to Giuliani, 8 or 9 to McCain, 1 to Huckabee and Brownback, but by giving Romney a 4 or 5, I could do what I wanted to. Approval voting just doesn't have the flexibility.

BROKEN LADDER said...

But what matters isn't how expressive your ballot is, but how satisfying the election results are to you. Approval Voting has a very low Bayesian regret, so it will statistically make you happier than methods like Borda and IRV.

To illustrate the fallacy more concretely, imagine a voting method where you rate all the candidates on a 0-100 scale, and then the winner is the candidate who got the highest average if we only consider the highest scores on all ballots. That is effectively identical to plurality voting in the election result. Maybe it made you feel warm and fuzzy all over that you got to express yourself over a range, but the election outcome still sucks for you.

So in order to understand why your criticism of Approval Voting is wrong, you have to convince yourself that the election result matters more than the joy you got from filling out and casting your ballot.

Opinionator said...

If you really insist on the Bayesian Regret value as a criterion, see the Wikipedia article on "Range voting." It is clear that, as low as approval voting is (in the simulations cited), range voting is still far better.

But you haven't answered my question as to what I should do about a candidate that I want to help only in the case where it turns out to be between him and someone I really hate, but not if it comed down to a decision between him and a candidate I prefer.

BROKEN LADDER said...

If you really insist on the Bayesian Regret value as a criterion, see the Wikipedia article on "Range voting."

I don't "insist", it is the criterion. It measures how well a voting system represents what voters wanted. I added the stuff about utility to the Wiki entry.


It is clear that, as low as approval voting is (in the simulations cited), range voting is still far better.

Of course it is, as I said. I suggested an experiment to specifically address that fact, which led to the creation of this page:
http://rangevoting.org/ShExpRes.html

My point was not that Range Voting gets better the smaller the range (Approval Voting being a "range" of only 2 values). My point was that your criticism of Approval Voting was flawed.

But you haven't answered my question as to what I should do about a candidate that I want to help only in the case where it turns out to be between him and someone I really hate, but not if it comed down to a decision between him and a candidate I prefer.

If you're trying to vote strategically like this, then Range Voting is the same as Approval Voting. Here's a page I co-authored that should answer your question more fully.
http://rangevoting.org/RVstrat6.html

Opinionator said...

You say, "I don't 'insist', it is the criterion. It measures how well a voting system represents what voters wanted." In fact, there is no uniformly accepted criterion; if there were, there would not be a major controversy over whether one or another voting system is best. As it is, Brams, Saari, Dummett, et al. differ sharply.

You also say, "If you're trying to vote strategically like this, then Range Voting is the same as Approval Voting." But the point I was making is that in the specific case I cited, there is no obvious way to cast my vote under approval voting, but there is under range voting. So you are totally wrong.

Now, with a modification of approval voting that was discussed on a page you referenced, approval/disapproval/no opinion voting, I might be satisfied. But not with approval voting as described by Brams, which I've always understood as approval voting strictly defined.

BROKEN LADDER said...

Bayesian regret is the objective way of measuring the quality of a voting method. The goal of a voting method is to maximize the sum of the voters' satisfaction with the outcome. This means that the social utility function is "additive", and is essentially proven to be the correct function. If you have any doubts about that, I challenge you to propose a superior alternative function -- and I'll bet that you cannot.

You are confused about what it is that guys like Brams and Saari are debating. Their arguments hinge on speculation about voter behavior and strategy, as well as the frequency of various paradoxes. The ultimate concern is still Bayesian regret, but they disagree about what kinds of tactics voters will use, and how problematic various criterion failures are (e.g. non-monotonicity).

Warren Smith's Bayesian regret calculations deprecate their speculation by simulating millions of random elections, with all sorts of different tunings of basic parameters, like amount of voter strategy and ignorance, number of candidates, and other factors -- and looking at the cumulative effect of all those problems and paradoxes.

So again, Bayesian regret is the right measurement. If Brams or Saari think the simulations are insufficiently realistic in their assumptions of voter strategizing or other factors, they are welcome to suggest improvements (and the source code is open). But that Bayesian regret is the correct metric is not under any kind of serious doubt.

...the point I was making is that in the specific case I cited, there is no obvious way to cast my vote under approval voting, but there is under range voting. So you are totally wrong.

No. The obvious way to vote with Approval Voting is to draw a threshold of acceptability, and approve every candidate you like above that threshold.

But your concern was that you might inadvertently approve or disapprove both of the front-runners, making your vote effectively useless. So your problem here isn't that it's hard to cast a sincere vote with AV, but that it's hard to cast a strategic vote. But a strategic vote is the same with RV and AV, so your criticism is flawed.

Now, with a modification of approval voting that was discussed on a page you referenced, approval/disapproval/no opinion voting, I might be satisfied. But not with approval voting as described by Brams, which I've always understood as approval voting strictly defined.

But your dissatisfaction would be a result of your own ignorance of the logical fallacy in your argument against AV.

wds said...

I have no problem with your original post. Brokenladder has an unfortunate tendency to argue 100X too much. A graphic about Bayesian regret (basically from Poundstone's book) is here:
http://rangevoting.org/BR52002bw.png

I hope you will "endorse" range voting (click endorse on the rangevoting.org web page & fill out the form) and try to correct common errors out there, e.g. see how many myths you can spot in this typical puff piece:

http://media.www.themacweekly.com/media/storage/paper1230/news/2008/02/29/Opinion/Instant.Runoff.Voting.Would.Strengthen.Democracy.St.Paul-3240970-page2.shtml

Anonymous said...

Range voting's challenge is that it violates norms of majority rule -- candidates with 45% could defeat candidates with 55%. It would make the Electoral College system for picking presidents even look kinda sensible, which sure takes some doing.

BROKEN LADDER said...

Anonymous,

Every voting system violates majority rule, depending on the circumstances. Nobel prize winning mathematician Kenneth Arrow is known for elaborating on that mathematical paradox. The simplest example is where you have a preference cycle where X is preferred by a majority to Y, and Y is preferred over Z, and Z is preferred over X. No matter who you think is the right winner, you've passed up another candidate who beat the winner by a majority.

The fact that such a scenario is even possible refutes the "majoritarian" notion that candidate X is necessarily better than candidate Y if preferred by a majority to Y. This is elaborated on here:
http://rangevoting.org/CondorcetCycles.html

The right way to measure the quality of a voting method is to calculate its Bayesian regret, to see how well it will satisfy voter preferences. After all, the point of voting is to obtain a satisfying election result, and get the most pleasing candidate you can get for your particular ideology. To turn down range voting in favor of some less utilitarian method is to decrease your own happiness with election results -- as well as the overall happiness of society. That doesn't make sense, and such intellectually empty arguments as "range voting violates majority rule" don't fly once you actually study social choice theory.

Clay Shentrup
San Francisco, CA
206.801.0484
clay@electopia.org

Anonymous said...

Approval and Range are related in the sense that in competitive elections Range easily becomes Approval like. An efficient strategy is to give 0 or max points to all candidates.

I propose to check also Condorcet and form your opinion on it.

Juho Laatu

Opinionator said...

First of all, the point about my comments regarding Bayesian regret is that any calculation of Bayesian regret has to make some ad hoc prediction of how many elections will divide in certain ways. The Wikipedia article used a series of simulations, and the numbers would, of course, be different if the elections were run again.





Broken Ladder's remark that I "might inadvertently approve or disapprove both of the front-runners, making [my] vote effectively useless" misconstrues my objection to approval voting. My objection is a different one. I am concerned that in a typical election, there are mid-level candidates, and I don't know whether to approve them or not. If I do approve them, and if the front-runners are one of those mid-level candidates and one of my preferred candidates, I effectively hurt my preferred candidate. However, if I do not approve them, and if the front-runners are one of those mid-level candidates and one of my disliked candidates, I effectively help my disliked candidate. So I end up having to make a guess as to which of the two scenarios is most likely to occur (a show-down between a mid-level candidate and one I like better, or one between a mid-level candidate and one I hate). That is my objection to approval voting.





Juho Laatu mentioned Condorcet voting. My main objection to that is that it often is not decisive: cycles can occur where A beats B, B beats C, and C beats A. So one needs to devise tie-breaking schemes, and when you include them, the system becomes excessively complex.

Opinionator said...

I assume that "wds" is the same Warren Smith that did the simulations summarized in Wikipedia. I did "endorse" range voting yesterday, even before wds's comment posted here.



It was Poundstone's book that got me interested in range voting, and I certainly believe that this is the right way to go. But I'm concerned by people who consider approval voting as a step in the right direction -- in some elections it can help, but in others it is a bad way to go. I think Poundstone's book makes that clear. I think most multi-candidate elections fall into the category where approval voting leads to problems: where there are "mid-level" candidates that I don't really like, but don't hate eitger.

benham said...

opiniontor,
What do you think of Range with a 0,1,2 ballot (or Approval with a voter option to "half-approve", or Approval-minus-Disapproval with a voter option to do neither)?

What about "Condorcet//Approval"?

Voters rank only candidates they "approve". Equal-ranking allowed. Elect the Condorcet winner if there is one, otherwise elect the approval winner.

Is that too complex in your view?

Why does IRV "leave you cold"? I live in Australia, and for US single-winner elections I think all the methods I've mentioned are good reform proposals.

BROKEN LADDER said...

First of all, the point about my comments regarding Bayesian regret is that any calculation of Bayesian regret has to make some ad hoc prediction of how many elections will divide in certain ways. The Wikipedia article used a series of simulations, and the numbers would, of course, be different if the elections were run again.

No. The simulations used millions of random elections summed together to get an average of the possibilities. There were 720 combinations of 5 basic parameters, and hundreds of thousands of random elections were done for each combination. Also there were different models used for distributing utility. All kinds of variables were tweaked, and Range Voting beat the other common methods in all 720 different models. So your notion that Smith's figures are too limited and do not account for other types of scenarios is wildly off the mark.

Look - Smith did these calculations originally in 2000, and has done subsequent simulations to address similar criticisms and assess very specific aspects of election methods. Your criticism is nothing novel, and has already been addressed. The simulations were substantive and informative, not just a shot in the dark.

I am concerned that in a typical election, there are mid-level candidates, and I don't know whether to approve them or not.

In Range Voting, you can have a candidate who is "between" a 5 and a 6, and you don't know which to give him. Same thing. You think about it for awhile and then you move on. What do you think Siskel and Ebert did when a movie was right on the line? Perhaps it takes a bit more thought (an important reason why hot-or-not chose Range Voting over thumbs up/down approval-style), but that's a tiny consideration compared to the massively more representative results you get.

A woman I spoke to in the Green Party once made a somewhat related criticism about IRV and Approval, based on the 2000 election. She said that with Approval, she might approve Gore and Nader, but she would hate doing that because it wouldn't allow her to say that she liked Nader more than Gore. Whereas IRV would have let her say that. But that is incredibly naive, because she's worrying about the ballot casting process instead of the result. If she knew better, she'd understand that IRV would encourage Nader supporters to bury Nader, to prevent Nader from being a spoiler (yes, IRV still has spoilers), whereas Approval Voting would not do that. So therefore Approval Voting would be fairer to Nader -- even if it didn't let this lady express that she liked Nader better than Gore. So my point to you is that

1) Yes, Range Voting is better with a greater-than-2-point scale, e.g. 0-10 instead of 0-1.

2) But Approval Voting is still an excellent voting method that beats IRV and Borda and probably Condorcet, and that may be more practical to implement, and then may help transition to Range in the future.

If I do approve them, and if the front-runners are one of those mid-level candidates and one of my preferred candidates, I effectively hurt my preferred candidate.

In Range Voting, if you give a front-runner an honest 5, and then give your preferred front-runner an honest 8, you also hurt your preferred candidate, by not giving them a 0 and 10 respectively.

With Approval Voting, you may give that less liked candidate an approval, along with your preferred candidate, so it's worse for you than sincere Range. But you also may give that "5" candidate a disapproval if he's right on the line, and then give the "8" candidate an Approval -- which helps your preferred candidate maximally. So that statistically evens out pretty much.

So I end up having to make a guess as to which of the two scenarios is most likely to occur (a show-down between a mid-level candidate and one I like better, or one between a mid-level candidate and one I hate). That is my objection to approval voting.

If you're making a guess about which is more likely to occur, then you're voting strategically, in which case you have the exact same problems as with Range. If you were voting "honestly", you'd just have some threshold of acceptability and approve every candidate above that line, without thinking about whether that would be strategically optimal for you; and that may hurt you, but it may also help you, as I demonstrated. Your objection continues to be about strategic voting, although you do not realize it.

Juho Laatu mentioned Condorcet voting. My main objection to that is that it often is not decisive: cycles can occur where A beats B, B beats C, and C beats A. So one needs to devise tie-breaking schemes, and when you include them, the system becomes excessively complex.

Well, relatively speaking, Condorcet is already pretty complex, so the tie-breaking systems don't add much more complexity. The problem for Condorcet is more of a utilitarian one, because of strategic burial problems. Also its overall complexity (regardless of tie-breaking) makes it infeasible for the real world.

BROKEN LADDER said...

'm concerned by people who consider approval voting as a step in the right direction -- in some elections it can help, but in others it is a bad way to go.

"Good" and "bad" is not a binary thing. The issue is how good or bad are election results, on average. And maybe also in the "worst case" and "best case" scenarios (i.e. we probably wouldn't want to use a voting method that had great average outcomes, but occasionally elected the worst possible candidate).

No matter which voting method you use, there are times that it will pick a worse result than a much worse voting method. For instance, it appears that Barack Obama is going to be our next President (thank god almighty). And an online Range Voting mock election I held, that began about 16 months ago, has Barack Obama winning among about 5400 voters. And looking at the overall results, it's clear that the "net roots" make vastly more intelligent candidate choices than the average voter. So there's a very good chance that Obama really is the social utility maximizer -- and yet he's probably going to win with our incredibly horrible voting method. Some times you just get lucky. And other times unlucky.

So to say there are scenarios where Approval Voting would not be so great doesn't really seem to say much of anything. The fact is, it would be hard for AV to be worse than plurality in almost any situation. And despite occasions when it may pick worse outcomes than Range Voting, it appears to do exceptionally well on average, without really ever having drastic results -- again, it can't really be worse than plurality in any realistic scenario.

So I urge you to really get past your intuitive distaste for Approval Voting, and look at the hard fact about it, and realize that it's a pretty damned good system.

BROKEN LADDER said...

Benham,

What the heck are you talking about? IRV certainly leaves you cold. It is effectively about as bad as plurality as it doesn't break two-party duopoly -- and so you still generally have two choices. And it increases the rate of spoiled ballots, and increases fraud susceptibility because it has to be centrally counted and invites the adoption of electronic voting machines.

IRV is a terrible voting method, period.

Anonymous said...

There are some rather complex Condorcet completion methods but there are simple ones as well. The simplest Condorcet method is maybe one that simply counts the least number of additional votes needed to win all others (called "minmax(margins)"). I'd say this is simple, and no separate tie-breaking scheme is needed since the definition above already covers everything.

Plurality can be counted by hand. Approval voting is maybe still doable as well. Range and Condorcet typically need machines to assist in the counting process (too much work for hand counting if the election is large).

I'm still a bit puzzled about why Approval would be bad and Range would be good. In competitive elections they may give quite similar outcome. If the elections are not competitive then Range gives a very different outcome (whose utility can be said to be much better than that of Approval). Do you maybe assume voters to be non-competitive? (not typical in political elections) Or do you assume that the small difference between Approval and Range in competitive elections is big enough to make Approval bad and Range good?

The reason why I proposed to consider also Condorcet is that it is quite strategy free in typical large public elections (more so than most other common methods). There are some situations where strategic manipulation is possible but they are relatively difficult to identify and use and risks of backfiring strategy are relatively high. When compared to Range the difference is that in Range there is practically always an incentive to exaggerate and vote in Approval style (which also leads to Approval style results). If you don't like the results of Approval, from this point of view Condorcet might bring better results than Range.

Juho

BROKEN LADDER said...

Plurality can be counted by hand. Approval voting is maybe still doable as well. Range and Condorcet typically need machines to assist in the counting process (too much work for hand counting if the election is large).

Baloney! Counting a "9" on a Range Voting ballot is mathematically no different than counting a "1" 9 times.

I'm still a bit puzzled about why Approval would be bad and Range would be good. In competitive elections they may give quite similar outcome.

His criticism was not about their outcomes -- that was precisely the problem I cited with his criticism. His criticism is based on the ballot casting process. Did you actually read what he wrote?

If the elections are not competitive then Range gives a very different outcome (whose utility can be said to be much better than that of Approval).

That is only true if you define "competitive election" as one in which lots of Range Voting users will be strategic. That's a false definition. A competitive election will certainly tend to increase the amount of strategic voting, but even in the most contentious of elections it's reasonable to expect fully half the voters to cast a sincere or nearly sincere ballot with Range Voting. So RV can still make a big difference in competitive elections.

Do you maybe assume voters to be non-competitive? (not typical in political elections)

97,488 voters voted for Nader in Florida alone in the 2000 election. I voted for Ron Paul in the CA primary. Some people just like to express themselves with their vote -- and Range Voting appears to draw out their expressiveness instinct.

http://rangevoting.org/Honesty.html
http://rangevoting.org/HonStrat.html

Also, even for competitive voters a sincere Range Voting ballot is pretty "competitive" as it is.
http://rangevoting.org/RVstrat6.html

You talk like you've never read about this subject before, despite the fact that you regularly participate in the Range Voting discussion group.

Or do you assume that the small difference between Approval and Range in competitive elections is big enough to make Approval bad and Range good?

What makes you think the difference is small? What evidence we have about voter psychology/behavior massively contradicts you.

The reason why I proposed to consider also Condorcet is that it is quite strategy free in typical large public elections (more so than most other common methods).

Yes you routinely make that bogus claim, which is totally unsupported by fact. We have lots of evidence that rank-order voting methods inspire voters to naively bury strong opponents to their favored.
http://rangevoting.org/AusAboveTheLine07.html

And this can cause a horrendous result with Condorcet:
http://rangevoting.org/DH3.html

Now you counter this with "Why would voters use a strategy that screws them all over?" But that question is trivially answered by the prisoners' dilemma -- both prisoners want to confess and get 5 year sentences, rather than both keep their mouths shut and get 1 year sentences.

There are some situations where strategic manipulation is possible but they are relatively difficult to identify and use and risks of backfiring strategy are relatively high.

This is wrong, as has been explained to you numerous times. A general strategy is to raise your favorite front-runner and bury the other. There is stong evidence this is statistically/strategically advisable, plus lots of voters will just naively do it regardless -- a fact which you consistently ignore.

And your talk about the risk that a strategy will "backfire" shows ignorance of the prisoners' dilemma. The point is that if enough voters bury, then a "bad" candidate actually wins. But that doesn't mean that it's not in each individual voter's best interest to bury.

When compared to Range the difference is that in Range there is practically always an incentive to exaggerate and vote in Approval style (which also leads to Approval style results).

That's not a "difference", since their is also an incentive to bury in Condorcet, even though you pretend like there's not.

If you don't like the results of Approval, from this point of view Condorcet might bring better results than Range.

Evidence supports the belief that something like 30-50% of Range Voting users will be sincere, which is enough to outperform Condorcet with a small amount of buriers.

No matter how much you ignore the evidence that refutes you, it's not going away.

Anonymous said...

Broken Ladder had a lot of comments. I propose to handle those details at the election methods and range voting mailing lists as usual in order not to ruin this blog with the details.

My recommendation to all is still not to listen to any flavour of propaganda but to find out oneself. Wikipedia is one quite good and reasonably neutral source of information on these topics.

Juho

benham said...

I classify what I consider to be good single-winner voting methods in 3 mutually exclusive categories:

(1) those in which voters never have any incentive (in terms of effect on the result) to vote their sincere favourites below equal top.
http://nodesiege.tripod.com/elections/#critsf

(2) those that meet the Condorcet criterion

(3)those that meet both Later-no-Harm and Later-no-Help.
http://nodesiege.tripod.com/elections/#critlnharm

The case for LNHarm goes: "We know that most voters are content or at least resigned to only voting for a single candidate because if they weren't there would be far more dissatisfaction with FPP evident than there is. Obviously if all the voters refuse to reveal any of their below-strict-top rankings then we can't elect anyone more representative (of the voters' sincere preferences) than the FPP winner. So it is very nice to able to guarantee to voters that giving a second preference can never reduce the chance that the candidate they ranked top can win, and giving a third preference can never reduce the winning chances of the candidates they ranked first and second, and so on."

In my view it is desirable that LNHelp and LNHarm be in balance, i.e that adding a lower preference is equally likely to help as to harm higher preferences. Methods that fail LNHarm but meet LNHelp
(like Approval,Range,Bucklin) give the voters strong incentive to truncate (i.e. conceal some of their below-top sincere ranking).

Methods that meet LNHarm but not LNHelp have a "random fill" incentive, and winners who owe their win to capricious or strategic lower preferences could lack legitimacy. The method would be open to ridicule from supporters of FPP, Approval etc., and the charge "the supporters of this method just want it so they can get their candidate elected by trickery/manipulation".

The best method in category (3) is IRV (i.e the Alternative Vote with unlimited strict ranking from the top allowed. Until one remains, eliminate the favourite, among remaining candidates,of the fewest voters.)

In terms of properties/criteria that I (and others,but perhaps not broken ladder)think are of some value/use, IRV is not dominated by any other method.

It is true that unlike Approval and Bucklin and some Condorcet methods it fails Minimal Defense.
http://nodesiege.tripod.com/elections/#critmd

But in terms of criteria that give guarantees about the majoritarian representativeness of the winner it is vastly better than FPP (aka plurality).

It meets Majority for Solid Coalitions (i.e. if more than half the voters vote a subset S of candidates above all others then the winner must come from S),

Mutual Dominant Third (i.e. if more than a third of voters vote a subset S of candidates above all others, and all the members of S pairwise beat all the non-members, then the winner must come from S),

Condorcet Loser (a candidate that pairwise loses to all other candidates can't win).

The incentive to to use the Compromise strategy (vote some compromise candidate above your sincere favourite to help that candidate defeat a greater evil) is much weaker than it is with FPP.

Enough for now. I'll wait for opinionator to answer my questions.

benham said...

Oops! Sorry opinionator, I see you
have "answered my questions" in separate new threads listed under Blog Archive for March 2008:

modified approval voting

"leaving me cold"