Gervase Lam--
You wrote:
Ignoring the names of any voting methods for a brief moment, here are some what I think are correct definitions in terms of candidates:
I reply:
Ok, but remember that those are _your_ definitions, and people aren't incorrect if they use those terms differently.
You continued:
Cardinal Ratings are a set of scores that range from 0 to 1. 1 means perfect, 0 means the EXTREME worst. By definition, it is possible for no candidate to get a 0 or 1.
I reply:
By _your_ definition. Who else said that 1 means perfect and 0 means the extreme [possible] worst? If you conduct a CR balloting, you could specify that if you want to, but you mustn't say what those terms should mean other than in a balloting whose rules you've specified.
Of course there's no reason at all why the range should be 0 to 1. 0 to 100 allows fine distinctions without the need for fractions. It's like 0 to 1, except that we don't all have to write a decimal point.
When we here conduct CR ballotings and write ratings, we mean 0 as the worth of the worst candidate and 100 as the worth of the best candidate. Your definition isn' t more vallid than that one. In fact, your definition requires the concept of the perfect candidtate, and the even more difficult-to-define notion of the worst conceivable candidate. Our definition of 0 and 100 is more concrete and easy: The worst and best candidates in the election.
You continued:
Cardinal Utilities (i.e. Social Utilities) are a set of scores that range from 0 to 1. 1 is given to the best candidate and 0 to the worst.
I reply:
Only if we happen to choose that numberng system, the 0 to 1 numbering.
You continued:
The other candidates are given scores in between the best and worst candidates as appropriate. This is your ExaggerateCR.
I reply:
You or Ken Johnson can define anything you want, but please understand that defining something a certain way doesn't mean that others should go by that definition, if they're already using a different definition.
Youi could call 100 the utility of the best candidate and 0 the utility of the worst one. But understand that, in the CR balloting, we have _ratings_, which aren't necessarily utilitiles. Sure, we ask people to rate sincerely, and, if they do, then the ratings represent the voters' best estimate of utilities. By the way, apparently we all rated sincerely in the EM presidential poll. In fact apparently none of us used strategy even in the Approval balloting. That's a good thing. Maybe we wouldn't strategize even in an actual public political Approval election.
You continued:
Ordinal Utilities is the same as ranking.
I replyi:
Only if the rankings are sincere. It's incorect to make those statementsthat you made, because it's possible for a ranking or rating to not be sincere--even though they were all sincere in the EM presidential poll.
You continued:
See <http://en.wikipedia.org/wiki/Utility> for details.
I reply:
A wikepedia is a good thing, because it lets everyone express their opinion and have it recorded, but of course you can't go by whatever someone says. I haven't checked the place that you quote above.
Yo continued:
Note that when the Cardinal Ratings Method is talked about, it is assumed that the ballots cast are Cardinal Utilities!
I reply:
Only by your own new definition. By your definition we're using the terms wrong. But we were using those terms as we use them before you posted your own definition.
The ballots cast have cardinal ratings, in which the voter rates each candidate from 0 to 100, with 0 representing the worst candidate, and with 100 representing the best candidate.
You continued:
By the way, can anybody explain the following statement from the above Wikipedia web page:
"The concept of cardinal utility suffers from the absence of an objective measure of utility when comparing the utility gained from consumption of a particular good by one individual as opposed to another individual. For this reason, neoclassical economics abandoned utility as a foundation for the analysis of economic behaviour, in favour of an analysis based upon preferences [i.e. rankings]."
In the terms of my definition of Cardinal Ratings, does this mean that "perfect" cannot really be defined?
I reply:
"Perfect" is difficult to define, and "worst possible" is even more difficult to define. I suggest that "best and worst among the election's candidates" is a lot easier to define.
The quote that you quoted is true of course: Your feeling about how good the best candidate is and how bad the worst one is might be more or less extreme than someone else's.
Whether we define 0 and 100 as worst possible and perfect, or best and worst of the election's candidates, it remains true that it's difficult to compare how much goodness or badness goes with a particular point assignment.
You couild say that making 0 be the worst conceivable and 100 be perfect makes the point assignments be more about something that's comparable among voters. But it's questionable what those terms mean, especially "worst conceivablly possible". Better to stick with best and worst of the candidates in the election, even though different people may have different notions of how good the best one is and how bad the worst one is. At least then we know pretty well what the voter means, as opposed to trying to guess what "worst conceivable" and "perfect" mean.
So sure, there's a problem in trying to compare different people's ratings. But adding up sincere CR ratings is still worthwhile and interesting, when the allowed extremes are the best and worst candidates, something with a clear meaning.
Mike Ossipoff
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