Re: [EM] What is the ideal election method for sincere voters?
On Sun, 2007-03-04 at 23:41 -0500, Abd ul-Rahman Lomax wrote: > Let's consider the method of deriving social utility from individual > utilities to be a detail. There seems to be some general agreement > that simple summing is not without value, but it is also clear that > summation is a simplification and that some other function may be > more ideal. However, political reality may intrude. Summation has a > history, more complex functions don't, as far as I know. > This isn't quite true. There's a whole field of study in welfare economics about different social welfare functions. "Indifference Curves" are defined as the curves where the social utility function is held at some constant - moving towards a higher indifference curve, then, is a social improvement. There are MANY possible indifference curves, however they all have a few things in common. Imagine that we set my utility and your utility as x-y axes, and then start plotting the social utility indifference curves for some given social welfare function. By definition, these indifference curves can't intersect (since that would mean some utility combination of me and you has two different social utilities) Anyway, for any reasonable social utility function: *Moving away from the origin should put us on a higher indifference curve (or at least keep us on the same one) - this is a pareto improvement. *Indifference curves should be convex - ie, taking both our utilities and averaging them should land us on a higher (or the same) curve. There are likely a few others that I'm forgetting. Anyway, there are two extremal indifference curves that meet these criterion. The first one is simple summation, as you noted. Another is taking the minimum of our two utilities - a so-called "Rawlsian" indifference curve (Since Rawls was a philosopher who insisted that the only way to judge societies was by their worst off.) These two extremes serve as bounds for reasonable indifference curves passing through a given point. There are an unlimited number of curves between them, and some are even named by welfare economists. A good example would be a hyperbola passing through the point we've selected. > I don't think that Condorcet methods were developed to maximize > utility; rather I think that the idea of the pairwise winner was seen > as intuitively correct. In fact, if all voters are fully informed and > aware of the general status, that is, the opinions and strengths of > preference of others, Condorcet methods should actually be ideal. > Range, however, is what collects this information more directly, a > ranked poll only, sometimes, approximates it. > It's quite possible that Condorcet methods maximize a reasonable social utility function, or that they at least do so "on average". Thanks, Scott Ritchie election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] it's pleocracy, not democracy
At 03:29 PM 3/4/2007, Juho wrote: >Single winner at its >purest is just electing one of a number of candidates, giving no >consideration to if it was the same voters that last time got their >way through. Basic single winner methods maybe have worse utility >than ones that take distribute the power over a sequence of >decisions, but I'd still allow use of word "democratic" to describe >them. Sometimes it makes sense to just forget the history. If the goal is making the best decisions, altering the method so that some specific group "gets its way" would seem less than ideal. It's noise. There can be some value in noise in control systems. A noisy system may be able to find states that would escape one that was running on a fixed and accurate program. However, that is probably unusual as a benefit. What *is* important is that in public choice systems there be *some* flexibility. How, indeed, it occurs to me to ask, are we to know who "got their way" in a secret ballot system? The presumption might be that the "way" was gotten by a party. It would be just my luck that by the time I wised up and became a Republican, the Democrats would get their turn. (Make no assumptions about my personal politics from this.) The system actually works better than it would work otherwise because people shift allegiances. Somehow in this discussion it seems to have been presumed that "the majority" is some fixed group of people, such that it is unfair to "the minority" for the majority to always win. Readers may know that I favor Range Voting as an election method, which does not automatically choose the preference of the majority, for it considers preference strength, if the voters choose to express it. I've said it before and I'll probably say it again: The majority properly has the right of decision, but it wisely exercises this carefully, with consideration of possible harm done to minorities. And everyone is a minority of some kind or at some time. election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] What is the ideal election method for sincere voters?
At 08:51 AM 3/4/2007, Juho wrote:
>On Mar 3, 2007, at 9:06 , Abd ul-Rahman Lomax wrote:
>
>>If we cannot agree on the best method with sincere votes, we are
>>highly unlikely to agree on the best method in the presence of
>>strategic voting, though I suppose it is possible
>
>Range is good with sincere votes. Its utility function (sum of
>individual utilities) is good. I think there are however also other
>good utility functions that can be used depending on the election and
>its targets. Therefore it is maybe not necessary to "agree on the
>best method with sincere votes".
Let's consider the method of deriving social utility from individual
utilities to be a detail. There seems to be some general agreement
that simple summing is not without value, but it is also clear that
summation is a simplification and that some other function may be
more ideal. However, political reality may intrude. Summation has a
history, more complex functions don't, as far as I know.
As I've mentioned, there is already an adjustment made in individual
values, typically, we may generally assume, some kind of
normalization. The normalization may cover some of the inaccuracy in
summation. For example, the distribution of wealth such that a single
person gets all the wealth gives the same sum in economic value
(let's neglect the other issues!), but when it is normalized and each
person's utility has the same Range, summation favors spreading it
out. That is, with N voters, more than two,
(N - 1) * 1 + 0 > (N - 1) * 0 + 1.
Even though the underlying absolute utilities were equal in sum.
Indeed, this would seem to favor robbing the rich few and giving to
the many poor, but that's only true if the rich have sufficient
wealth to make a significant difference to the poor. I'd suggest that
this is only likely to happen in a seriously unjust society. And
that, of course, is a whole other question.
The fear that in a democracy the people will automatically seize the
wealth of the rich and redistribute it is, I think, not valid in a
mature democracy. It may be valid under conditions of mob rule, or
the equivalent, rule by demagogues whose real goal is power and/or
wealth for themselves.
>Let's say we are selecting pizzas (A,B). There are three voters whose
>preferences are (9,6), (9,5) and (0,6). Pizza A is the best selection
>according to Range.
Which is why, of course, small groups would be advised to use Range
only as a polling device. And, indeed, with large groups, I've
suggested that Range polls be ratified, because under conditions like
this, the majority, which properly *does* have the power of decision,
may wish to do something other than maximize the raw, undeliberated
Range values.
> I can however imagine that when selecting a pizza
>the intention could be to have nice time out with friends. The third
>voter obviously hates the A pizza. Maybe we should use some other
>utility function, maybe one that maximizes the worst utility to any
>individual voter. This kind of a method would select pizza B.
Absolutely, simple summation can fail. If somehow we could express
absolute utilities, and include the mutual effects, since voter
utilities are *not* independent variables, summation would be
correct. But we have, usually, no way of doing that. If the choice is
one where economic effects are the sole consideration, the summation
may be ideal; and where a choice deprives an individual entirely,
it's possible that this person would be compensated by the others.
I.e., that loss would be covered by an indemnity. And this would be
factored into the utilities.
(If an action benefits many and harms few, it may take only a small
loss for the many to restore the few to a proper level of benefit.
The proper goal is to maximize the sum, and the sum is not some fixed
number. It is conceivable that a true consensus action can be found,
one with high utility, or at minimum no harm, for *all*.)
>It is also questionable if it always makes sense to select the
>favourite alternatives of those votes that have strong feelings and
>not to respect the opinions of voters with milder feelings that much.
If we were deciding a series of choices, and the "strong" and "mild"
feeling voters were always the same people, then, I'd suggest, as the
strong got their way each time, the "mild" voters would begin to
consider themselves unjustly deprived. They would become strong in
their feelings and votes. Unless they agreed that that the "strong"
getting what they want was just.
>In some election it may make sense to give each voter same weight.
>One could either normalize the votes or accept the one man one vote
>principle (= weight of each opinion is 1.0). (Note that e.g. in the
>Condorcet methods weight of each expressed preference ("X is better
>than Y") is exactly 1. That does not take into account different
>preference strengths of different voters but gives all opinions the
>same weight.)
Yes. It is clea
[EM] Juho--Strategy-resistance
Juho said: >I very much support evaluating also the performance with sincere votes / >the utility function that a methods tries to implement (in addition to >evaluating its strategy resistance). I reply: Often, when people speak of methods in terms of strategy, they speak of "strategy-resistance", as if the goal were to have a methat that could withstand strategy, defeat strategy. Actually, the fundamental strategy problem is not that a method doesn't defeat or resist strategy. The problem is that it forces strategy. The problem is that a method creates strategy dilemma for voters, that it creates a need for some degree of giveaway strategy in order to enforce majority rule or keep someone worse than the CW from winning. As I've said, yes the better method don't let offensive strategy cause a need for drastic defensive strategy. But that's a secondary concern, merely part of meeting the goal in the paragraph before this one. Mike Ossipoff election-methods mailing list - see http://electorama.com/em for list info
[EM] Juho--Margins fails Plurality. WV passes.
Juho-- In a posting to a different mailing list, Markus pointed out that margins fails the Plurality Criterion, and that wv Condorcet passes the Plurality Criterion. For me, Plurality isn't essential. For instance, I consider MDDA a good proposal. But if we're going to have the added definition-wordiness of Condorcet, we should get what Condorcet can offer, including compliance with the Plurality Criterion, SFC, GSFC, and SDSC, and URNEC. Mike Ossipoff election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] very simple email poll
At 07:26 AM 3/4/2007, Jobst Heitzig wrote: >Hello folks, > >I would be very glad if all of you would take one minute's time to >answer this very simple email poll! Well, the problem with ad-hoc polls is that the answers depend on the questions, and ask the wrong questions, you'll get misleading answers. >Consider a situation with three options A,B,C and only two voters, >whose ratings* are as follows: > >voter 1: A 100, C 50, B 0 >voter 2: B 100, C 50, A 0 > >Now please answer these three questions with "yes" or "no": > >1. Is C socially preferable to A? ___ If we accept the conditions stated as below, that there is no more information, there is absolutely no way to tell. However, considering general conditions and a peer society, it is highly likely that the preferable option is C. This is because the utilities are so drastically different. If, for example, the options are: A 1 gets all the food, 2 starves B 2 gets all the food, 1 starves C both get enough It's pretty clear that option C is generally preferable. But what if option C is that both die, since there is only enough food for one person. This is a zero-sum game, and, let me suggest, it is not one which is generally soluble with an election method Real elections and real choices are, far more often, not zero-sum games. Nor are the utilities so drastically opposed; we will see such expressed utilities in Range Voting, but this is because of normalization and magnification. It is generally assumed that people won't want to make choices that push all the chips into one corner, and it is assumed that people *may* behave as if this is what they want, because, with rule of law, it won't actually happen. Usually. We allow and even encourage self-interest, justified by an assumption that pursuit of self-interest results in common good. It's obviously an assumption that does not hold under all conditions. Faced with the election scenario, I wonder what would happen if 1 and 2 sit down and talk. Why in the world would two people use a Range election method to actually make the decision? Especially given such opposing utilities? Rather, these people need to seek better solutions than A, B, and C. They might exist. >2. Is tossing a coin to decide between A and B socially preferable to A? ___ It might be perceived as fair. Let's look at this situation in another way. Let's assume that the utilities are normalized. Actually, on an "absolute" scale, the ratings would look like this: voter 1: A 18, C 17, B 16 voter 2: B 18, C 17, A 16 Sum of utilities is the same no matter what choice is made. Now, here is the paradox: if we assign a value to "fairness," to these two voters feeling that they were treated fairly, such that neither resents the other, we might see A or B as being inferior to C. But why was this not reflected in the ratings? Given the conditions of the problem, and assuming that the ratings are made *with knowledge*, we are stuck. Looking from the outside of this system, I might think that C is better because then A and B aren't likely to fight. But, of course, this utility may have been incorporated into the ratings. Other things being equal, though, my instinctive reaction is that C is the best solution. However, if both voters consent, then the coin toss may be better. It depends on what these choices are and how important they are. Even if they are life and death, choosing the one who drops off the lifeboat has often been done by drawing straws. >3. Is C socially preferable to tossing a coin to decide between A and B? ___ *If* it is perceived as fair by 1 and 2. >*If you want, you may interpret the ratings as the best information >we have about "individual utility". I considered this and played with it. election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] it's pleocracy, not democracy
On Mar 2, 2007, at 12:40 , Jobst Heitzig wrote: > [sorry if this comes twice, but it didn't seem to get thru the > first time] > > Dear folks, > > some clarification because in recent posts democracy and majority rule > were confused quite often... > > In a dictatorial system, almost all people have no power. > In a majoritarian system, up to half of the people have no power. > In a democratic system, ALL people HAVE some power, that is, "the > people rule". > > Hence, majoritarian systems in which a majority of 50% + 1 voter can > make all decisions are NOT democratic. The greeks called them > "pleocratic". > > Can a system be democratic? > Can it even be democratic without using significant randomization? > > If we are faced with a whole sequence of decisions instead of only > one, > we could distribute the power over all decisions in the sequence: I'd maybe call this a specific kind of proportionality, serial proportionality or proportionality in time. Single winner at its purest is just electing one of a number of candidates, giving no consideration to if it was the same voters that last time got their way through. Basic single winner methods maybe have worse utility than ones that take distribute the power over a sequence of decisions, but I'd still allow use of word "democratic" to describe them. Sometimes it makes sense to just forget the history. Maybe electing the best film of the year is one example. It doesn't matter much even if the same people liked the best film of this year and of last year. Another example could be starting a genocide. Even if few percent of the voters would like that, it maybe is not the best option to start it after a sufficient number of years/elections have passed. Different elections may have different targets. Sometimes "consensus", "compromise", "least opposition", "acceptability" or "wide support" could be key criteria instead of "proportionality". But this type of methods are good for places where proportionality is the way to go. > Naive solution: assign each decision to a (different) single voter so > that each voter decides something in turn and hence all people have > some > power. Obviously, there are many deep problems with this. > > More sophisticated solution: > > Remember for each voter in what fraction of the decisions so far the > voter's then-favourite option has been elected; call this that voter's > "actual success rate". > > Also remember for each voter the average (over all decisions so far) > fraction of voters that had the same then-favourite as the voter at > hand; call this that voter's "to-be-expected success rate". > > Now, in each decision, elect that option which minimizes the sum of > squared errors between the voters' current to-be-expected success rate > (including the current decision) and the voters' resulting actual > success rate if that option were elected. In the long run, this sum of > squared errors should converge to zero (remains to be proven), so this > method can be called "asymptotically" democratic. > > For example: Assume a sequence of A/B-decisions, voter 1 votes > always A > and voters 2-4 vote always B. Then the following would happen: > > to-be-expected actual success sum of > round success rates winner rates afterwards squared errors > 1 .25 .75 .75 .75 B0 1 1 11/4 > 2 .25 .75 .75 .75 A.5 .5 .5 .5 1/4 > 3 .25 .75 .75 .75 B.33 .67 .67 .67 1/36 > 4 .25 .75 .75 .75 B.25 .75 .75 .75 0 > 5 .25 .75 .75 .75 B.2 .8 .8 .8 1/100 > 6 .25 .75 .75 .75 A.33 .67 .67 .67 1/36 > 7 .25 .75 .75 .75 B.29 .71 .71 .71 1/196 > 8 .25 .75 .75 .75 B.25 .75 .75 .75 0 > ... How would you count the actual and to-be-expected success rates of new voters that vote at round n but that have not voted before (if this method is expected to cover such cases)? > A little mathematics shows that this method is equivalent to a kind of > "weighted plurality" in which each voters vote is weighted with the > following (not necessarily positive) history-dependent weight: > (current to-be-expected successes) - (earlier actual successes) - 1/2 > > The latter indicates a potential problem: Knowing my success rates so > far, I may deduce that my vote in the current decision is actually > negative, in which case I may have incentive to vote for the strongest > competitor of my favourite instead of for my favourite. Another strategy could be to vote one's worst competitor if one's own favourite candidate is already expected to win in any case with sufficient margin. This way one could try to collect more weight for the next election. One approach is to have a formula that carries only positive weight to the next election. And one more approach is to tie the carried weight to the parties
Re: [EM] very simple email poll
From: [EMAIL PROTECTED] > Consider a situation with three options A,B,C > and only two voters, whose > ratings* are as follows: > > voter 1: A 100, C 50, B 0 > voter 2: B 100, C 50, A 0 > > Now please answer these three questions with "yes" or "no": > > 1. Is C socially preferable to A? ___ Yes. C has the same inherent utility, but also has additional utility due to being less likely to cause social friction due to protests or other public disorder. > 2. Is tossing a coin to decide between A and B socially preferable to A? ___ Probably yes. By giving B some chance at winning, there is less likelihood of social friction being generated. B's supporters will know that they fairly lost and also that they could win at the next election. OTOH, A and B are equal, so tossing a coin just adds randomness to the process. Since risk can be cheaply created, there will always be an oversupply of risk. If a government is based on coin tosses, the markets will be hit with a random forcing every election. That will happen anyway though. > 3. Is C socially preferable to tossing a coin to decide between A and B? ___ Yes. C is better than A or B and is thus better to a random choice of A or B. Raphfrk Interesting site "what if anyone could modify the laws" www.wikocracy.com Check Out the new free AIM(R) Mail -- 2 GB of storage and industry-leading spam and email virus protection. election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] What is the ideal election method for sincere voters?
On Mar 3, 2007, at 9:06 , Abd ul-Rahman Lomax wrote:
However, if we assume sincere voters, what is the ideal election
method, or the best among the options we know?
I very much support evaluating also the performance with sincere
votes / the utility function that a methods tries to implement (in
addition to evaluating its strategy resistance).
However, is Range ideal with sincere voters? If not, why not?
It is at least good.
And, please, explain to me why a method that will work well for
selecting pizzas, with sincere votes, will not work well selecting
political officers, similarly with sincere votes. If you think that.
If we cannot agree on the best method with sincere votes, we are
highly unlikely to agree on the best method in the presence of
strategic voting, though I suppose it is possible
Range is good with sincere votes. Its utility function (sum of
individual utilities) is good. I think there are however also other
good utility functions that can be used depending on the election and
its targets. Therefore it is maybe not necessary to "agree on the
best method with sincere votes".
Let's say we are selecting pizzas (A,B). There are three voters whose
preferences are (9,6), (9,5) and (0,6). Pizza A is the best selection
according to Range. I can however imagine that when selecting a pizza
the intention could be to have nice time out with friends. The third
voter obviously hates the A pizza. Maybe we should use some other
utility function, maybe one that maximizes the worst utility to any
individual voter. This kind of a method would select pizza B.
It is also questionable if it always makes sense to select the
favourite alternatives of those votes that have strong feelings and
not to respect the opinions of voters with milder feelings that much.
In some election it may make sense to give each voter same weight.
One could either normalize the votes or accept the one man one vote
principle (= weight of each opinion is 1.0). (Note that e.g. in the
Condorcet methods weight of each expressed preference ("X is better
than Y") is exactly 1. That does not take into account different
preference strengths of different voters but gives all opinions the
same weight.)
You also questioned the vulnerability of Range to strategic voting.
Approval style voting may be either sincere or strategic. Let's say
that X and Y go out for pizza. All the pizzas are quite ok to both
but X is a bit selfish and wants to make the decision on which pizza
to order. Voting strategically in bullet style makes perfect sense to
him. The worst outcome is to toss a coin on which one's favourite
pizza to take. If Y votes sincerely, X will decide.
Using Condorcet or other more majority oriented methods instead of
Range may either be a result of favouring more strategy resistant
methods (and corresponding utility functions) or sometimes also a
direct result of electing the most applicable utility function.
In addition to the viewpoints tat I discussed above there are at
least the proportionality cosiderations, both with multiple winners
and single winners distributed over time, but I understood that these
already fall out of the scope of your mail.
Juho
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Re: [EM] weighted voters, success rate
Are we supposed to understand what Warren wants to say with this? > re puzzle 33 at http://rangevoting.org/PuzzlePage.html > the answer is > W_K = const * (2 P_K - 1) / (4 P_K [1-P_K]) > > wds > _ In 5 Schritten zur eigenen Homepage. Jetzt Domain sichern und gestalten! Nur 3,99 EUR/Monat! http://www.maildomain.web.de/?mc=021114 election-methods mailing list - see http://electorama.com/em for list info
[EM] very simple email poll
Hello folks, I would be very glad if all of you would take one minute's time to answer this very simple email poll! Consider a situation with three options A,B,C and only two voters, whose ratings* are as follows: voter 1: A 100, C 50, B 0 voter 2: B 100, C 50, A 0 Now please answer these three questions with "yes" or "no": 1. Is C socially preferable to A? ___ 2. Is tossing a coin to decide between A and B socially preferable to A? ___ 3. Is C socially preferable to tossing a coin to decide between A and B? ___ Thank you very much! Jobst *If you want, you may interpret the ratings as the best information we have about "individual utility". _ In 5 Schritten zur eigenen Homepage. Jetzt Domain sichern und gestalten! Nur 3,99 EUR/Monat! http://www.maildomain.web.de/?mc=021114 election-methods mailing list - see http://electorama.com/em for list info
