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Social Choice and Beyond
Thursday, April 3, 2008
Range Voting and Arrow's General Impossibiliity Theorem
Mood:  incredulous
Now Playing: Wagner: Der Ring des Nibelungen
Topic: Range Voting

The position taken by the Center for Range Voting regarding Arrow's General Impossibility Theorem is, I believe, that it doesn't apply to utility based systems and, therefore, range voting "escapes" Arrow's conclusion. I believe a much stronger position should be taken: that Arrow intends that his General Impossibilty Theorem DOES apply to range voting and that range voting refutes it. Certainly, Arrow's Theorem is valid given certain assumptions, but I don't believe that it's "general." Instead it should be called Arrow's Special Impossibility Theorem since it only applies to ranking procedures. Arrow certainly considers utility based systems and claims that they are invalid given his acceptance criteria. Consider the following quote from pp. 32-33 of "Social Choice and Individual Values":

"It may be of interest, however, to consider a particular rule for assigning utility indicators to individual orderings. Assume that the individual orderings for probability distributions over alternatives obey the axioms of von Neumann and Morgenstern; then there is a method of assigning utilities to the alternatives, unique up to a linear transformation, which has the property that the probability distributions over alternatives are ordered by the expected value of utility. Assume that for each individual there is always one alternative which is preferred or indifferent to all other conceivable alternatives and one to which all other alternatives are preferred or indifferent. Then, for each individual, the utility indicator can be defined uniquely among the previously defined class, which is unique up to a linear transformation, by assigning the utility 1 to the BEST CONCEIVABLE alternative and 0 to the WORST CONCEIVABLE alternative. This assignment of values is designed to make individual alternatives interpersonally comparable.

"It is not hard to see that the suggested assignment of utilities is extremely unsatisfactory. Suppose there are altogether three alternatives and three individuals. Let two of the individuals have the utility 1 for alternative x, .9 for y, and 0 for z; and let the third individual have the utility 1 for y, .5 for x and 0 for z. According to the above criterion, y is preferred to x. Clearly, z is a very undesirable alternative since each individual regards it as worst. If z were blotted out of existence, it should not make any difference to the final outcome; yet, under the proposed rule for assigning utilities to alternatives, doing so would cause the first two individuals to have utility 1 for x and 0 for y, while the third individual has utility 0 for x and 1 for y, so that the ordering by sum of utilities would cause x to be preferred to y.

"A simple modification of the above argument shows that the proposed rule does not lead to a sum-of-utilities social welfare function consistent with Condition 3. Instead of blotting z out of existence, let the individual orderings change in such a way that the first two individuals find z indifferent to x and the third now finds z indifferent to y, while the relative positions of x and y are unchanged in all individual orderings. Then the assignment of utilities to x and y becomes the same as it became in the case of blotting out z entirely, so that again the choice between x and y is altered, contrary to Condition 3.

"The above result appears to depend on the particular method of choosing the units of utility. But this is not true, although the paradox is not so obvious in other cases. The point is, in general, that the choice of two particular alternatives to produce given utilities (say 0 and 1) is an arbitrary act, and this arbitrariness is ultimately reflected in the failure of the implied social welfare function to satisfy one of the conditions laid down."

Clearly, Arrow is setting up the rules so as to produce NORMALIZED range votes which violates his own assumption that 1 should correspond to the BEST POSSIBLE alternative and 0 to the WORST POSSIBLE alternative. Had he actually used UNNORMALIZED range voting, the ratings for x and y would not have changed and this would have lead to a contradiction of his theory.

However, his theory would still apply to ranking procedures. My point is that Arrow's GENERAL Impossibility Theorem is not general at all but in actuality is a SPECIAL Impossibility Theorem. This deflates Arrow's balloon and should encourage those seeking new forms in political science and economics. I think the Center  for Range Voting should maintain that range voting invalidates or refutes Arrow's GENERAL Impossibility Theorem.


Posted by jclawrence at 2:35 PM PDT
Updated: Thursday, April 3, 2008 2:41 PM PDT
Saturday, July 14, 2007
Discussion on Range Voting Blog between Mr. Lomax and Myself
Topic: Range Voting

This discussion took place on the Range Voting blog:

 --- In http://groups.yahoo.com/group/RangeVoting/, Abd ul-Rahman Lomax <abd@...> wrote:
>
> At 01:15 PM 7/4/2007, jclawrence2 wrote:
> >--- In http://groups.yahoo.com/group/RangeVoting/, Abd ul-Rahman Lomax <abd@>
> >
> > > If we image that everyone has this rubber band,
> > > then stretching it until all are the same length
> > > is equivalent to normalizing the extremes of
> > > attraction and aversion. This is what I referred
> > > to as the first normalization. A particular
> > > election does not utilize the full length of the
> > > band, but only a portion of it; the utilized length varies from
> >voter to voter.
> >
> >This is where we differ.
>
> We don't differ, at least not in this. Rather, Mr. Lawrence's concept
> is incomplete. If reality is A + B, and one person states that, and
> another says, "reality is B," do they differ? Perhaps. But only if
> the second says, "There is no A."
>
> Mr. Lawrence has well explained it here:
>
> >  I would make the max and min points of each
> >voter's rubber bands correspond to each voter's most favored and
> >least favored candidates, respectively.
>
> This is the second normalization that I referred to. If I apply that
> transformation, I end up with what Mr. Lawrence uses.

There are two realities here, and we need to be clear which one we are talking about. One is

the actual process that an actual voter goes through when he is composing a range ballot for

an actual election. The second is the computer simulation. Model A (Abd's model) assumes that

each voter will place each candidate on a cardinal preference scale from his particular

absolute worst to his particular absolute best candidate. Then the voter will normalize this

scale to the max and min of the range voting scale, i.e., 99 and 0 if that is the chosen

range with the absolute best at 99 and the absolute worst at 0. This results, however, in a

partial strength vote. If the voter wishes to have a full strength vote he will normalize

again so that his most favored actual candidate is at 99 and his least favored is at 0. Note,

however, that if a voter wants a full strength vote, he need only derive his cardinal voting

preferences without the absolute scale and normalize once to the max and min of the voting

range.


Notice that  Model B (my model) assumes that each actual voter will place each candidate on a

cardinal preference scale where the only meaning is the preference orderings and preference

intensities or the length of the gaps between candidates. There is no meaning attached to the

most favored or least favored candidate's position on this scale relative to an absolute

scale. There is no meaning attached to the strength or weakness of his preferences or

utilities. Then the range votes are derived by normalizing each voter's preference or utility

scale to the max and min range votes, i.e., 99 to the max candidate and 0 to the min

candidate (if that is the scale used).

The second reality is the computer simulation. Here we randomly generate a utility for each

voter-candidate pair. In Model A we first have to randomly generate the end points

corresponding to the actual (as opposed to the absolute) best and worst candidates. If the

minimum utility is 0% for the absolute worst candidate (and 100% for the absolute best) we

need to come up with some percentage for the actual worst and some percentage for the actual

best. These are the end points. Since we have no information to go on, we need to generate

these numbers randomly. So we have to assume some probability distribution over end points.

This introduces an arbitrary assumption. Then once these end points are determined, we have

to randomly generate the utilities which attach to the candidate-voter pairs. These utilities

are equally likely or uniformly distributed over the range from actual worst to actual best.

For instance, if the actual worst utility for voter 1 is a% and the actual best utility for

voter 1 is b%, then voter 1 would have a randomly generated equally likely utility for each

actual candidate somewhere between a and b. These utilities would then be used to compute

Bayesian regret. The actual numerical range votes would be determined by assigning b% 99

votes and a% 0 votes (if that is the vote range) and interpolating in between for the other

candidates.

For model B I propose a different computer simulation. A uniform distribution of utilities is

assumed over all the candidates because each candidate is equally likely to have a utility at

any point on the scale between 0% and 100%. For each voter one candidate (randomly chosen)

will be placed at 0% and one at 100%. For the rest of the candidates a utility is generated

for the voter-candidate pairs which is assumed to have a uniform distribution between 0% and

100%. No end points need be computed. The maximum possible social utility would be achieved

if every voter got his first place choice as winner. This is in general not achievable except

in a special case. The actual social utility would be computed for the computer generated

voter-candidate-utilities. It will depend on the statistical distribution of utilities over

the voter-candidate pairs. The regret would then be the difference between the social utility

if everyone got their first place choice as winner minus the actual social utility. This

would then be averaged over many simulated elections. This figure could then be used as a

figure of merit and compared to other voting methods.

>
> >  You would make the end points
> >correspond to each voter's ideal best and ideal worst candidates,
> >respectively, who are not even on the ballot. This gives rise to two
> >models. Let's call them model A (your model) and model B (my model.
>
> Model A precedes model B.

No, Model A exists in its own right and Model B exists in its own right.

> Let's consider the rubber band as something
> that exists internally for the voter, entirely aside from the
> particular election. The voter then comes to consider a set of
> candidates, and places the candidates on the band. Does the voter
> utilize the entire band?
>
> Normally, not. The "entire band" i[n] model A.
>
> Now, the actual internal reality is something like a combination of
> these two. People don't have fixed ratings for candidates, rather, in
> fact, they do, quite likely, end up with model B, and fairly
> directly. But these bands, fixed by ratings of the extreme candidates
> in the actual candidate set, are not related to each other.
>
> Warren, in his utility simulations, if I'm correct, generates random
> utilities for each candidate, placing them on a *complete* band.

If these utilities are generated in such a way that they tend to cluster around the midpoint

of the band and fall off towards the extremes of absolute best and absolute worst, then it 

is assumed that the utility for the average candidate for each voter is at the midpoint of

the band. In general this is not true.
 
> If the voters vote those untransformed utilities, we get minimized
> Bayesian Regret. But, in fact, we expect that many or most voters
> will normalize the votes, by tying the extreme candidate positions to
> 0% and 100% Range votes. This is a normalization, what I called the
> second normalization, and it loses information, particularly by,
> potentially, distorting weak preferences, making them seem strong.
> This is how utility maximization leaks from standard Range. It's
> still quite good, but it can be better.

I would argue that in reality the only data the system has regarding the utility of the

voters in an actual election are the range votes themselves. You don't have any utility

information on any absolute scale. You can only measure social utility in any meaningful way

relative to the actual votes cast, and the figure of merit would be the summation over all

voters of  the difference between maximum and actual individual voter utilities. For example,

if max utility is 100% and the candidate actually elected represented a utility of c% (c

greater than or equal to 0) for voter i, then summation over i would represent social utility

and 100% minus this sum would equal Bayesian regret.

The simulation for Model B then would be entirely analagous to what could be measured in an

actual election. Assuming only full strength votes, each voter's max and min candidates would

be chosen randomly and then the other utilities would be randomly generated assuming a normal

probability distribution from 0% to 100%.

>
> > > If the voters take the utilities from this
> > > normalized band and express them linearly, we end
> > > up with something like maximized social utility.
> > > But this is not how voters will actually vote.
> > > This is "honest true utility" voting, and it
> > > does, in fact, happen informally in deliberative
> > > process in functional societies. People *do*
> > > express mild preferences as mild preferences,
> > > when they are being honest and open with each
> > > other. And, yes, doing so means that those
> > > preferences will not be considered with the same
> > > weight as strongly expressed preferences. Which is exactly as it
> >should be.
> >
> >I don't agree. Some people have strong preferfences about everything.
>
> So? Some people only have strong preferences when they have clear
> knowledge. In a democracy, we allow people to determine for
> themselves what their preferences are, and how strong they are.

Even assuming honesty, there is no good reason for anyone to submit anything less than a full

strength vote. If a voter has limited knowledge, he can defer to a recommendation from

someone he trusts. Isn't that what your work on delegable proxy is about, Abd? He can

delegate portions of his vote to someone he chooses. Not assuming honesty, only the savvy,

sophisticated and "in the know" voters would vote a full strength vote, and they would tend

to get their way at the expense of the weaker voters. Is this what you really want: a system

that lets the more sophisticated exploit the less sophisticated? I would think that you would

want to eliminate such tendencies rather than enshrine them. That's what we have today!

>
> >Does that mean they should always get their way?
>
> If everyone else has weak preferences, yes.

I think this point is debatable. In a democratic voting system one of the hallmarks is

equality of inputs.Letting people with stronger preferences have more sway in the voting

system is tantamount to giving them more votes and people with weaker preferences less votes.

>
> >  For instance, my
> >girlfriend and I go to the movies. She has her preference for which
> >movie we should see and I have mine. But she always claims to really,
> >really, REALLY want (and need!) to see her movie.
>
> You reveal a great deal about yourself.

Not really. See below.

>
> >  The world is going
> >to come to an end if she doesn't get to see her preferred movie while
> >I would like to see my preferred movie but I can't claim the world is
> >going to end if I don't get to see it. Does this mean that we should
> >always see the movie of her choice? I don't think so. I think
> >everyone's preferences should count as much as everyone else's.
> >That's the principal of fairness.
>
> Then what in the world are you doing supporting an SU method, which
> makes strong preferences count for more than weak?

Actually, I support Model B which makes all voter's inputs have equal strength.

>
> And, by the way, I'd suggest resolving some issues with your
> girlfriend. You could spend the rest of your life in misery if you don't.

This was an entirely fictitious example, but I appreciate your concern, Abd, for my mental

health.

> >
> > > >  After all utility is
> > > >simply a way of attaching numbers to preference info. Then if you
> > > >wanted to set one end point equal to 100 range votes and the other
> > > >end equal to 1 range vote, you could figure out the numerical
> > > >relationships for all alternatives in between as far as voting is
> > > >concerned.
> > >
> > > Sure. However, unless by "end point" you mean the
> > > maximum and minimum utilities for the set of
> > > candidates in the election,
> >
> >I do.
> >
> >this becomes the
> > > second normalization.
> >
> >In model A this is the second normalization. In model B this is the
> >one and only normalization.
>
> Sure. And thus it floats with the candidate set, and the full range
> for each voter differs in preference strength from the full range for
> every other voter. This results in loss of SU accuracy.

It depends on your interpretation of SU. I submit that SU as measured based on the actual

votes in an actual election is the only meaningful SU. And the simulation for Model A does

not correspond to reality. It assumes knowledge of what goes on in a voter-bot's mind. And

the figure of merit is higher the more votes you assume are less than full strength. I think

it's a positive thing when all voters vote full strength for reasons mentioned above.

Therefore, the figure of merit should be higher not lower! So I have problems with the

validity of the simulation.
 
> >  > >  Actually, you could do this without ever stretching the
> > > >rubber bands to the same length. Just make the end points (1,100)
> >for
> > > >each individual voter. The range votes will always come out the
> >same
> > > >whether or not a linear transformation is applied to any or all
> > > >individual preference info.
> > >
> > > That is "stretching the rubber bands to the same
> > > length." What we are doing is expressing position
> > > relative to the extent of the rubber band.
> > >
> >
> > > > > Absolute Vote utilities (which are Absolute utilities
> >normalized to
> > > >a
> > > > > scale from absolute best to absolute worst of the whole
> >universe of
> > > > > choices, not just those appearing in an election)? Then these
> >are
> > > > > "converted" to Range votes. By whom? How?
> >
> >Model A would have the voters specify cardinal preferences on an
> >absolute scale where the max and min end points are the absolute best
> >and absolute worst candidates (who are not in general on the ballot)
> >FOR EACH VOTER. Thanks for clarifying that.
>
> You are welcome. If you read the material on the simulations, you
> would realize that the way the preferences and ratings are generated does this.

For reasons stated above, I don't agree that the simulations are valid.

>
> >  Model B would have the
> >voters specify cardinal preferences on a scale where the max and min
> >end points are each voter's most preferred and least preferred
> >candidates of the candidates actually in the race. These could be
> >converted to range votes by the voter or by the system. Perhaps if
> >the voter's cardinal preferences were expressed by placing dots on a
> >line or by moving a slider on a computer display, this in itself
> >would constitute the "vote." From there the system would process the
> >information.
>
> Model B, as stated, does not allow voters to weaken their vote. Why?
> What is the social benefit? Or, for that matter, the individual benefit?

Equality of vote strength is a hallmark of democracy. And it doesn't allow savvy voters to

get their way at the expense of "suckers" who vote a less than full strength vote.

> > > >I don't think there is a need for an absolute scale, just a
> > > >specification by each voter on some scale.
> > >
> > > "Need" according to what purpose? If we want to
> > > maximize social utility, or the overall
> > > satisfaction of society, we are attempting to
> > > maximize something that we assume is comparable.

If each vote has equal strength, then the satisfactions of each voter are comparable and

social utility is computed in a different way. Model B has a different definition of social

utility than does Model A. Model B still is utility maximizing - just a different definition

of utility.

> >
> >Model A attempts to maximize social utility. I have doubts as to the
> >validity of that since it favors those with intense preferences as in
> >the movie example I cited above.
>
> This is a common argument against Range Voting. Now, please explain
> why people with strong preferences should *not* be favored.

Every person deserves to have his vote have equal strength in a democracy. You think the

smarter people should be favored more because they know more and, therefore, have stronger

preferences. This is an elitist position. Even an imbecile deserves to have his vote count as

much as an Einstein in a democracy. He can use your methods and delegate his vote to a proxy,

for example. Only ignorant people would vote less than a full strength vote. Smarter people

would tend to get their way more often, and this does not mean that society would have more

utility only that smart people would have more utility. This is paternalistic.

>
> Strong preferences can come from various sources. On the negative
> side, they can come from bigotry, prejudice, ignorance, combined with
> arrogance. But on the positive side, they can come from knowledge.
> Imagine an omniscient voter. The voter *knows* what the various
> outcomes will do. And, if we assume that this voter cares about what
> happens, the voter will have very clear and very strong preferences.

Elitist. Paternalistic.

>
> There is a common moralistic judgement about strong preferences, and
> almost automatic assumption that they represent fanaticism and are
> thus to be ignored. I find it fascinating.
>
> Lawrence shows that he wants to get his way sometimes. Why? If he
> really doesn't care, and his girlfriend does, why should he insist?
> But, of course, he *does* care. Sometimes. And sometimes, then, he
> would have to express his real preference strength. He really does
> want to see *this* movie.
>
> Of course, he could go without her.

And sometimes I do. For instance, I saw "Sicko" the other night. She stayed home because she

thought it would be depressing.

>
> The situation he described is a setup. He is, he believes,
> easy-going, accommodating. She is hysterical and demanding.
>
> Yet, in fact, he is *not* easy-going. He resents her demands.

We usually work it out. We're going tonight to see "La Vie En Rose" together, and she will go

to see most chick flicks by herself. But, as I said, the example was entirely fictitious. A

less ad hominem response would have been more appreciated.

>
> What I ultimately came to in considering Range Voting is that we
> should assume that preference strengths expressed are real, that is,
> we should respect them, but we should also understand that the
> limitations of the system and the context mean that the expressed
> preferences can be distorted for various reasons. The enemies of
> Range use the possibility of distortion as a reason to not use the
> system, and they write of[f] strategic voting (voting approval style)
> with contempt, as if it is morally wrong. It's odd. Because it is
> morally wrong, the argument must go if expressed completely -- they
> never do it -- for a person to exaggerate preferences, we should use
> a system that equates all preferences, thus exaggerating some while
> devaluing others.

I'm not arguing against range voting. After all the only real difference between Model A and

Model B in an actual election is that in the former "weak" votes would be allowed and in the

latter all votes would have the same strength. Does that really invalidate Model B from being

considered range voting? And then I would argue for a different method for measuring voter

satisfaction or social utility or Bayesian regret, a different way of simulating elections

that is more or less equivalent to the measurements that could be taken for computing social

utility in an actual election.

>
> Does Lawrence know about Borda Count? It seems that he wants a ranked
> method....

Actually, I favor Range over Borda, but Range where all votes have the same strength.

>
> >Model A also favors "idealists"
> >whose preferences tend to span the full range from absolute best to
> >absolute worse as opposed to "realists" whose preferences tend not to
> >approach the extremes of absolute best and absolute worst. I'm
> >refering here to "honest" voters and not to strategic voters who
> >would tend to represent themselves as idealists.
>
> Lawrence has totally misunderstood what is going on. "Model A" is a
> simulation of what actually goes on in the mind of the voter.

I don't think what goes on in the mind of a voter is to place all actual candidates on some

absolute scale. Rather there are methods and algorithms using actual candidates for deriving

preferences and preference intensities. I think an actual voter would use these or just

interpolate between actual best and actual worst seat of the pants style.

>It's not a voting method, it's a simulation method. It doesn't favor anyone.
>
> *Voting* the "Model A" preferences (full range, including all
> possible virtual candidates), would be idealistic. But I certainly
> was not proposing that anyone vote that way. If we want to study
> utility maximization, however, we need to know some kind of
> commensurable ratings of the candidates, otherwise we are measuring a
> sometimes drastically distorted utility, where the mildest of
> preferences can loom as large as a live-or-die preference.

I'm assuming that in an actual election anything illegal could not be an alternative or

candidate. For instance, it could not be a legal election if one candidate ran on a platform

of genocide for some minority if he won. These shouldn't be life or death alternatives. And

the way the alternatives are structured has a lot to do with whether you might get freaky

results. So, yes, I would favor equal vote strengths for all voters regardless of whether

some voters thought they should have their way because their preferences were more intense

than others, and I would compute social utility from the baseline of equal vote strengths and

not based on an absolute scale.

>
> >What I am attempting to do in Model B is to take the arbitrariness
> >out of the process. The first step of that would be to eliminate the
> >first normalization in Model A. An appropriate metric for Model B can
> >be chosen for the purposes of comparing voting systems, but I would
> >probably shy away from claiming that it maximized social utility.

Actually, I would say it maximized social utility as defined.

> >I might say it maximized voter preference satisfaction but I'm
> >speculating a little. Don't nail me on this!
>
> What Lawrence is trying to do is to eliminate the information that
> shows us that pure Range is not absolutely ideal.

It depends on what you consider to be ideal, and you have to consider what can be actually

measured as opposed to what is a figment of your imagination.

>Indeed, he,
> apparently, would force voters to vote in such a way as to guarantee
> that utility is not maximized.

It depends on how you measure utility.

>It's actually quite arbitrary.

Well, I think Model A is arbitrary because it depends on voters using less than a full

strength vote in order to reveal what their utilities truly are. In Model B utilities are

revealed by the actual votes themselves and social utility is a function of the distribution

of preferences and preference intensities over the voters.

>
> What we prefer is to allow voters to decide how to vote. We [have] given
> them a tool, a means of expression, and we tell them how the
> information they express will be used. The *meaning* of it? We do not
> tell them that. They may tell each other that, various people will
> tell them that a 100% vote means this or that, and a 50% vote means
> this or that, but the system doesn't care what the votes "mean."
>
> It just adds up the numbers, or engages in other analyses.
>
> For example, if it is what I'm calling Range PW, the Range winner is
> determined by adding up the votes for each candidate. The candidate
> with the highest vote total is the Range winner, we might call this
> candidate the "nominee." Then the ballots are recounted, if
> necessary, to determine if any candidate is preferred to the nominee,
> i.e., beats the nominee in a pairwise ranked election using the Range
> ballots as data. It's fairly simple counting; because every pair
> involves the nominee, unlike Condorcet analysis, where every pair
> must be totalled. If no candidate beats the nominee, the nominee is
> elected. Otherwise there is a runoff election between the nominee and
> the candidate beating the nominee; since the Range winner is
> *usually* not beaten pairwise, this should be rare. (The question of
> what to do if two or more candidates beat the nominee, which should
> be extraordinarily rare, I'm not addressing at this point, though a
> complete method would have to consider that.)
>
> >I assume that the candidate that maximizes the amount of money in the
> >voters' (collective) hands should win the election. I would think
> >this would hold for Model B but not for Model A which would tend to
> >maximize the money in the hands of the idealists at the expense of
> >the realists, i.e., those who enjoyed the money more at the expense
> >of those who enjoyed the money less.
>
> Nonsense. Lawrence simply makes up arguments as he goes. We were
> discussing an economic Range election, and assuming honest voters.
> How much they enjoy their gains is irrelevant;

In social utility how much someone enjoys something certainly is relevant. Personal utility

is a function of enjoyment, satisfaction and a few other things.

> they simply express
> the value of each outcome. Why would one assume that this would
> concentrate wealth? What does "idealism" have to do with it?
>
> The election was not asking the voters how much they would enjoy
> their gains, but what those gains would be. It's an economic model,
> and it's useful because it shows how Range *does*, with honest
> voters, actually maximize overall social benefit. There is still a
> potential distribution problem, but that's a separate complication.
>
> (In theory, some outcome could supposedly make a single individual
> fabulously wealthy, but for this outcome to prevail, it must not
> steal this wealth from the many. Range is not zero-sum. In the
> imagination of Lawrence, the "idealists", presumably many of them or
> else it would not work, lose money and this is transferred to the
> necessarily few "realists," though it was completely unstated how
> personal philosophy was related at all.)
>
> Model A involves maximizing the *actual cash* in the voters hands,
> thus there is more to spread around. Model B maximizes differential
> cash. Model B might indeed take from the rich and give to the poor,
> because it may well overvalue cash in the hands of the poor (since
> the difference looms larger). The problem is that the overall wealth
> of society can thus decline. You can only soak the rich so far! And
> the benefit to the poor is necessarily small, since there are so many
> poor. It might be educational to consider what would happen if *all*
> the assets of the very rich were distributed. How much per person?
>
> And that's a one-time distribution. It wouldn't come again.

Could we stick to the basics? Bringing economic models into this is getting pretty far afield

especially when it isn't clear to me what your economic model is all about.

>
> >Well, it is another possible model. Call it Model C. In this model
> >everyone agrees on an "absolute best" and "absolute worst" instead of
> >their being different for each voter as in Model A.
>
> I don't think that Model A has been understood. Absolute best and
> absolute worst are *equated* for all voters in Model A.

This is not what you said above when you said that absolute best and absolute worst were

peculiar to each voter in Model A, i.e., each voter had his own absolute best and absolute

worst candidates not necessarily the same for each voter:

<quote:> >Model A would have the voters specify cardinal preferences on an
> >absolute scale where the max and min end points are the absolute best
> >and absolute worst candidates (who are not in general on the ballot)
> >FOR EACH VOTER. Thanks for clarifying that.
>
> You are welcome.
<end of quote>

> Every voter
> is presumed to have a measuring stick; the stick is of finite length.
> While we may imagine that it is a different length for each voter, we
> express preferences on that stick in terms of percentage of the
> length. So the extreme end of the stick in one direction is the
> absolutely most pleased that the voter could possibly be. There is no
> more satisfaction possible. And the other extreme is the worst
> possible outcome.
>
> The assumption is that human emotion is bounded. You can only get so
> happy and so unhappy. We rarely experience the extremes on the stick,
> so we might say that "I was so happy I could have burst!" But we
> don't burst. And we can be so unhappy that we decide to end it all.
> It can feel incredibly bad! But if something stops us from ending it,
> we were not crushed by the feelings, they were finite, it only seemed
> that they were endless and that the situation was hopeless.
>
> Anyway, the simulations assign utilities on this scale, for the
> candidates in the election. There is no assumption made that one
> candidate must occupy each end of the scale, for there is no basis
> for assuming that; in real life, such extreme preferences would be
> rare (I was about as opposed to Bush as possible by 2004, but I did
> not feel like committing suicide when he was officially elected, if
> we can call it that.)
>
> Thus the range of utilities for the candidate set vary from voter to
> voter. If voters were to vote the actual utilities, social utility is
> maximized.

I would argue that voters cannot even measure or compute their actual utilities only that

they can derive preferense and preference intensities according to some algorithm or seat of

the pants style. Social utility cannot be maximized based on something that's a figment of

the imagination.

> But we do not expect that they will. Rather, they will
> normalize to expand the range of ratings to fill the available range
> of votes. Some may not do this completely; these are "weak votes."
> They are allowed, and they are socially useful. But they are not
> recommended unless the voters preferences are truly weak. If there
> are two candidates, and you *really* like both of them, there is no
> reason why you should not vote 100 for both. It's effectively an
> abstention, but it expresses support and confidence in them, and
> allows others who *might* have preferences (for better or for worse,
> i.e., based on ignorance or knowledge) to prevail.

If a voter likes all the candidates extremely well, he can give them all 100s. If he dislikes

them all extremely and equally he can give them all 0s. Or give them all 50s. This tells

something about the voter but it doesn't affect the election.

> > > >  The problem with
> > > >that is not everytbody could agree on what the absolute scale
> >should
> > > >be. One person's pleasure may be another person's pain. Therefore,
> >it
> > > >seems preferable to me to take each person's specification of
> > > >preferences at face value and, for voting purposes, assign the same
> > > >value to every person's max candidate and vice versa for min.
> > >
> > > It may seem preferable to Lawrence because, for
> > > reasons which escape me, though I can speculate,
> > > he doesn't understand what is going on.
> >
> >The reason is *it takes the arbitrariness out of it!*
>
> It *adds* arbitrariness to it! But it appears that Lawrence isn't
> going to see this.

One man's arbitrariness is another's underlying principle and vice versa.

> > > What has been done, I believe, is to establish an
> > > internal set of utilities that take up positions,
> > > to use his analogy, on the rubber band. These
> > > utilities are distributed in a way that
> > > simulates, much better than mere random positions
> > > equally spread along the band, how people are
> > > really going to feel about candidates. By the
> > > nature of the simulation -- and in correspondence
> > > with reality -- candidates would only rarely
> > > approach the ends of the band.
> >
> >In Model A. In Model B they are the ends.
>
> And then comes a new candidate, declared at the last minute, better
> or worse than all the others. Suddenly the "end" of the band isn't the end!

This is a red herring. It's only the final vote that counts, and voters can reevaluate their

positions and change their votes if a candidate enters or leaves before the actual vote. If a

voter's vote changes before he actually votes, so be it.

>
> That doesn't happen with Model A. The new candidate simply takes up a
> new position on the band. All the other relationships remain the same.
>
> Model A is independent of irrelevant alternatives. Model B is
> sensitive to them. If we have a Range election, and A is going to
> beat B, introducing C can cause B to beat A, if the ratings are normalized.
>
> >[...] But if we peg
> > > the scales to the min and max candidate, the
> > > utilities for each candidate *will* vary with the
> > > candidate set (that is, a new max or a new min will shift the
> >utilities).
> >
> >True, but utilities will not vary if candidates which aren't max or
> >min enter or leave.
>
> Nor does it make any difference if Mars is retrograde. The point was
> that introducing a new candidate *can* shift utilities in such a way
> as to change the outcome *without* the new winner being the
> introduced candidate.
>
> If utilities are normalized.
>
> And we do expect them to be normalized, usually.
>
> I start few threads. One that I did start, fairly recently, was about
> "the obvious defect in Range Voting," and why it was also the best method.
>
>
> >Thank you, Abd, for clarifying this. I was assuming Model C which,
> >however, is a viable model and the one I think Warren uses in the
> >simulator.
>
> Warren uses Model A.

Maybe we should ask Warren.

> How the voters vote varies with the simulation.
> Using the utilities directly from Model A is what generates minimum
> Bayesian Regret, if I'm correct.
>
> Lawrence has confused voting strategy with the measurement of how the
> method works. What he calls "Method B" is a voting strategy, one of
> many possible.

No, Model B is a slightly different model than Model A. It has nothing to do with strategy.

Model A and the simulation thereof and the measurement of merit thereof is totally dependent

on strategy in the sense that it assumes a higher figure of merit if more voters vote

honestly, i.e., weakly, thereby ceding the strength of their vote to the more opportunistic,

dishonest and savvy voters.

>
> It's not entirely clear to me what Lawrence means by Model C. There
> is no external reference point, and, indeed, it is simply an
> assumption that max and min possible preference for everyone is to be
> equated. This is Model A, no more, no less.
>
> > > The "honest true utilities" are positions on the
> > > band, which includes the possibly unused extremes.
> >
> >That's Model A. Model B assumes that the end points are the max and
> >min candidates for each voter.
>
> Yes. However, Model B is a voting strategy, not a method for
> determining utility.

The sole difference between Models A and B is that Model A would allow "weak" votes and Model

B would make all votes full strength thereby guaranteeing equality of voter input for all

voters.
 
> > > In other words, there is something better than
> > > pure Range Voting. And Lawrence seems to be
> > > consistently avoiding acknowledging this, even
> > > though it is shown in the simulations.
> >
> >No problem with acknowledging there might be something better than
> >pure range voting. I'm just trying to pare down the process to the
> >bare essentials and not try to deal with all the sophisticated
> >variations right now.
>
> I think it would profit Lawrence to understand how the simulations
> are done. What is "the process?" There is a process used in the
> simulations for assigning utilities. There is a process for
> converting these to Range votes. The former can be varied, though I'm
> not sure how much it has been done, I think Warren uses an issue
> distance model for assigning utilities.

For now, can't we keep this simple? A randomly computed utility for each voter-candidate

pair? This is unnecessarily complicating the discussion.

The latter varies with the
> voting strategy. The only "strategy-free" conversion is the direct
> expression of the originally assigned utilities. Model A, to use the
> name we have been giving it here. Other voting strategies are used,
> including what Lawrence calls Model B. It's one of a number of them.

See above "The sole difference..." It has nothing to do with strategy.
 
> >If the voters just submitted their cardinal preference specifications
> >without numbers attached, i.e., dots on a line or sliders on a
> >computer display, then it would be moot whether they were submitting
> >a full or partial strength ballot. Again I'm trying to pare down to
> >essentials. I think the full or partial strength ballot issue is a
> >side issue I'm not really concerned with at this point.
>
> If there are sliders on a computer display, like slide
> potentiometers, then it is *not* irrelevant whether they submit a
> "full or partial strength ballot." It affects the outcome, and
> specifically it affects the power of the voter's vote. To avoid this
> -- some consider it a problem, I don't -- some would normalize all
> the votes. That is what Lawrence had suggested, and he seems to be
> continuing it here. The sliders would presumably correspond to a
> rating, so numbers would be involved, even if the voter didn't see
> the actual numbers. Normalizing all the votes is complex, far more
> complex than simple Range addition of votes. It would be difficult to
> do manually.

I don't know. It seeems fairly simple to construct a ballot on which a voter would place his

max and min candidates and then interpolate in between for the others. Both manual and

electronic versions would be straightforward.

>


Posted by jclawrence at 10:37 AM PDT
Updated: Saturday, July 14, 2007 10:42 AM PDT

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