Re: [Election-Methods] a strategy-free range voting variant?
4. For each option, determine the probability P(Y) of being a randomly chosen benchmark voter's favourite. These probabilities build the benchmark lottery. 5. Finally, the voting accounts are adjusted like this: a) Each deciding voter's account is increased by an amount equal to the total rating difference between the winner and the benchmark lottery amoung the *other* deciding voters, minus some fixed fee F, say 10*N^(1/2). (Note that the resulting adjustment may be positive or negative.) This is the part I understand the least. Let's imagine the following votes from the deciding voters: 10 million: Nader: 10 Gore: 5 Bush: 0 41 million: Gore: 10 Nader: 5 Bush: 0 49 million: Bush: 10 Gore: 5 Nader: 0 Let's say that the lottery winner was Bush. The real winner is going to be Gore, with 705 million voting money units, while Bush has only 490 million. The total rating difference is 215 million. Do you want to modify each deciding voter's account with that big amount? You can try to diminish this modification by the fixed fee but I guess the modification will still be very high, because you are not able to precisely predict the votes not to mention who the lottery winner is going to be. And I guess if you try to eliminate this huge voting money transfer by some averaging operation, you will bite your other finger by ruining the strategy-freeness. Even if these worries are valid, this random partitioning of the electorate looks a witty idea, worth some other trials. I also like the idea of voting money, but with some reservations; if the value of the voting money is not bound exactly to some real value, then good-bye, strategy-freeness, I guess. Otherways, voting money can be used even with the classical Clarke-tax. Yes, Clarke-tax goes to one direction, but every voter on every day can get one voting money unit. If my voting money does not grows (except by votings), I will use the most amount of it when I'm afraid to die soon - why keep them if I can't use them?. So there seems to be some extra voting power on the part of the deadly ill. Peter Barath Tavaszig, most minden féláron! ADSL Internet már 1 745 Ft/hó -tól. Keresse ajánlatunkat a http://www.freestart.hu oldalon! Election-Methods mailing list - see http://electorama.com/em for list info
Re: [Election-Methods] [english 92%] Re: a strategy-free range voting variant?
Dear Jobst Heitzig Your new strategy-free voting idea which you described here http://article.gmane.org/gmane.politics.election-methods/13693 (which is a fairly radically innovative new approach to Clarke-Tideman-Tullock voting, and I am CCing Ed Clarke and N.Tideman in this email) looks VERY interesting and might be an excellent idea. But I do not fully understand it yet and I think you need to develop+clarify+optimize it further... plus I'd like you to unconfuse me! Here are some questions (I quote you after then my questions about that quote follow, then repeat): Of course, this is far from being a new idea so far, and it is not yet the whole idea since it has an obvious problem: although it obviously manages to elect the better option (the one with the larger total monetary value), it encourages both the seller and the buyer to misrepresent their ratings so that the gap between R2(B)-R2(A) and R1(A)-R1(B) becomes as small as possible and hence their respective profit as large as possible. In other words, this method is not at all strategy-free. --QUESTION: if they make the gap small, then the buyer pays little to the seller. Yes, that is better for the buyer. But doesn't the seller have the opposite incentive? It is not clear to me the incentive you say exists here, really does exist. If it doesn't, then you do not need to fix this problem because there is no problem. It'd help to clarify this point. 5. Finally, the voting accounts are adjusted like this: a) Each deciding voter's account is increased by an amount equal to the total rating difference between the winner and the benchmark lottery among the *other* deciding voters, minus some fixed fee F, say 10*N^(1/2). (Note that the resulting adjustment may be positive or negative.) QUESTION: I'm confused about this whole benchmarking thing. You said the benchmark voters were being benchmarked, but now you say the deciding voters are being benchmarked. ??? What does total rating difference between the winner and the benchmark lottery among the *other* deciding voters MEAN precisely??? This is not clear english... the winner's rating is a number but the benchmark lottery is not a number. You need two numbers. The compensating voter's accounts are decreased by the same total amount as the deciding voter's accounts are increased, but in equal parts. (This may also be positive or negative) --this seems to hurt poor voters. I.e. if there are rich voters who vote +-100 and poor voters who vote +-1 then the poor voters will need to pay the same fee in 5b as the rich voters. They may therefore have incentive to avoid being in the electorate at all, in which case the electorate will become biased (rich-dominated). Of course, it is no real money so maybe this does not matter. Everybody is initially equally rich. But perhaps that is itself a misrepresentation? and the benchmark lottery will tend to equal the ordinary random ballot lottery with all voters. --I do not understand what this means exactly. In particular, the method is quite efficient. --what does efficient mean? If the fee F is set so that the expected (in a reasonable model) adjustments of the individual accounts are all zero --well, I'm not sure what that means, but it seems like F can be readjusted every election so over a long sequence of elections accounts balance. Then F would not be fixed but it could be fixed in each election individually. Does that matter? Finally, if I'm not mistaken, the method is still strategy-free for these reasons: i) A benchmark voter's favourite mark does neither influence the winner nor the voter's own account, so there is no incentive to misstate the favourite. ii) A deciding voter's ratings do influence the voter's account only by influencing the winner; the same arguments as above show that it is optimal for a deciding voter to sincerely state her true ratings. iii) A compensating voter's ratings to not affect anything. Since you don't know in which group you end up, your optimal vote is the true ratings! --I think your basic ideas summarized here seem VERY promising, but as above I am confused about the details -- and even when I get unconfused there may be modifications that may be desirable. I would like to post this all as a web page on the CRV web site (credited to you of course) when things clarify, if you permit. --Warren D. Smith http://rangevoting.org Election-Methods mailing list - see http://electorama.com/em for list info
Re: [Election-Methods] [english 92%] Re: a strategy-free range voting variant?
To answer one of my own questions, if you alter the percentages - which you have the freedom to do - away from 1/3, 1/3, 1/3 to, say, deciders: 5% compensators: 90% benchmarkers (which I'm confused about): 5% then the compensators will have a fixed fee per capita which is small (about 18 times smaller than average). Therefore, my complaint that poor voters would have incentive not to vote leaving to a rich-dominated electorate, will be diminished. For practical purposes in large elections this should be an adequate fix of this problem (if it really was a problem). Designer has freedom to alter these 3 percentages to optimize real-world performance. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [Election-Methods] a strategy-free range voting variant?
Dear Warren,
you wrote:
But I do not fully understand it yet and I think you need to
develop+clarify+optimize it further... plus I'd like you to unconfuse me!
I'll try...
Of course, this is far from being a new idea so far, and it is not yet
the whole idea since it has an obvious problem: although it obviously
manages to elect the better option (the one with the larger total
monetary value), it encourages both the seller and the buyer to
misrepresent their ratings so that the gap between R2(B)-R2(A) and
R1(A)-R1(B) becomes as small as possible and hence their respective
profit as large as possible. In other words, this method is not at all
strategy-free.
--QUESTION:
if they make the gap small, then the buyer pays little to the seller.
Yes, that is better for the buyer.
But doesn't the seller have the opposite incentive?
It is not clear to me the incentive you say exists here, really does exist.
If it doesn't, then you do not need to fix this problem
because there is no problem. It'd help to clarify this point.
Isn't that the usual situation when bargaining? Given that the buyer
would be willing to pay more than the seller would minimally accept as a
price, the seller tries to maximize the price as long as he thinks the
buyer is willing to pay it, and the buyer tries to minimize her offer as
long as she thinks the seller is willing to accept it. So, both work to
minimize the gap between the demanded and the offered payment.
5. Finally, the voting accounts are adjusted like this:
a) Each deciding voter's account is increased by an amount equal to the
total rating difference between the winner and the benchmark lottery
among the *other* deciding voters, minus some fixed fee F, say
10*N^(1/2). (Note that the resulting adjustment may be positive or
negative.)
QUESTION:
I'm confused about this whole benchmarking thing.
You said the benchmark voters were being benchmarked, but now you
say the deciding
voters are being benchmarked. ???
That might be a language problem for my part. What I mean is this: In my
thinking, democracy demands equal decision power for every voter. Random
Ballot accomplishes this in a way, but is not efficient. But the Random
Ballot lottery can still serve as a benchmark for other, more
efficient choices. In my suggested method, the benchmark voters are
needed only to estimate what the Random Ballot lottery amoung all voters
would be. The individual ratings for the actual winner of the election,
who is only determined by the deciding voters, is then compared to the
individual ratings for this benchmark (i.e. of the estimated Random
Ballot lottery) in order to the individual transfers of voting money.
The higher a deciding voter rated the benchmark and the lower she rated
the winner, the more voting money is transferred to her account (or,
rarely, the less is transferred *from* her account).
In mathematical terms: Let p(X) be the probability of X being the
highest rated option when we draw one of the benchmark voter's ballots
uniformly at random. (So the p's define our benchmark lottery)
Let r(i,X) be the rating deciding voter i specified for X. Put
r0(i) := sum { p(X)*r(X,i) : X }
(over all options X), i.e., the expected rating deciding voter i
specified for the lottery outcome. Then put
t(X) := sum { r(X,i) : i }
(over all deciding voters i) and
t0 := sum { p(X)*t(X) : X }.
Assume W is the range voting winner of the deciding ballots, i.e.,
t(W) t(X) for all X other than W
Now the voting account of deciding voter i is changed by this amount:
sum { r(W,j)-r0(j) : j different from i }
(over all deciding voters j different from i),
which is equal to
(t(W)-t0) - (r(X,i)-r0(i))
The higher you rated the winner (i.e., the higher your r(X,i)) and the
lower you rated the average favourite of the benchmark voters (i.e., the
lower your r0(i)), the less voting money you get.
What does total rating difference between the winner and the
benchmark lottery among the *other* deciding voters MEAN precisely???
This is not clear english... the winner's rating is a number but
the benchmark lottery is not a number. You need two numbers.
It means
sum { r(W,j)-r0(j) : j different from i }
(see above).
The compensating voter's accounts are decreased by the same total
amount as the deciding voter's accounts are increased, but in equal
parts. (This may also be positive or negative)
--this seems to hurt poor voters. I.e. if there are rich voters who
vote +-100
and poor voters who vote +-1 then the poor voters will need to pay the same fee
in 5b as the rich voters. They may therefore have incentive to avoid
being in the electorate at all, in which case the electorate will
become biased (rich-dominated).
Yes, that might be a problem. So, being in the electorate (meaning
amoung the whole number of N voters) should not be something one can
choose. In other words, we put N to be the number of all eligible
voters, no matter whether they choose
Re: [Election-Methods] a strategy-free range voting variant?
Another small remark: With N voters total and B benchmark voters, the size D of the deciding group should probably be O(sqrt(N-B)). This is because the amount transferred to an individual deciding voter's account is roughly proportional to D times a typical individual rating difference, hence the total amount transferred to the deciding group is proportional to D² times a typical individual rating difference. The same total amount is payed by the group of at most N-B-D compensating voters. Each of them should not be required to pay more than a constant multiple of a typical individual rating difference, hence D²/(N-B-D) should be O(1). Jobst Election-Methods mailing list - see http://electorama.com/em for list info
Re: [Election-Methods] a strategy-free range voting variant?
i) A benchmark voter's favourite mark does neither influence the winner nor the voter's own account, so there is no incentive to misstate the favourite. --But it influences how much other people get paid or pay. If I hate Republicans, I might try to influence things to force Republicans to pay more and/or get paid less. Election-Methods mailing list - see http://electorama.com/em for list info
[Election-Methods] delegate cascade
Hello to the list, I'm a software engineer, currently developing an online electoral system. I was in another discussion (link at bottom) and a subscriber recommended this list to me. I have a few questions, if anyone is able to help. A key component of the electoral system (to explain) is what I call a delegate cascade voting mechanism. It is intended for use in continuous elections (open to recasting). The overall aim is to support consensus building. In this mechanism: ...a 'delegate' is a participant who both receives votes, like a candidate, and casts a vote of her own, like a voter. But when a delegate casts her vote, it carries with it those received. And so on... Passing from delegate to delegate, the votes flow together and gather in volume - they cascade - like raindrops down the branches of a tree. New voters are not restricted in their choices, but may vote for anyone, their unsolicited votes serving to nominate new candidates and to recruit new participants into the election. http://zelea.com/project/votorola/d/outline.xht I can only cite 3 references for the mechanism (Pivato, Rodriguez et al., and myself) all from 2007. Does anyone know of an earlier source? Is anyone else working with this mechanism? Have there been discussions along similar lines? Please bring me up to date, -- Michael Allan Toronto, 647-436-4521 http://zelea.com/ P.S. The other discussion thread (a broader topic) is: Read any useful research lately, unanswered research questions? http://groups.dowire.org/r/topic/6QthnRysw5lJmRGqnPAy5y Election-Methods mailing list - see http://electorama.com/em for list info
