Re: [Election-Methods] a strategy-free range voting variant?
Dear folks,
this night I had two additional ideas for RRVC, so here's two new
versions of it.
In the first version, the fee F is determined from the benchmark ballots
so that the expected price a deciding voter has to pay from her
voting account is just that voter's rating difference between the winner
and the random ballot lottery:
RRVC - New Version 1
0. Each voter i is assumed to have a voting account whose balance is
denoted C(i).
1. All N voters fill in a range ballot and additionally mark their
favourite in case of a top-rating tie. Voter i can use ratings
0...C(i) only. If C(i) is negative, she can use the rating 0 only
(but still mark her favourite). Let R(X,i) be the rating voter i
gave to option X.
2. Put D = sqrt(N) (rounded up), and draw D deciding ballots. For
each option X, determine the total rating T(X) these deciding
ballots gave to X. The winner W of the decision is that option whose
total rating is maximal, i.e. that option W for which T(W)T(X) for
all X other than W.
3. From the remaining ballots, draw D benchmark ballots. For each
option X, determine the total rating B(X) these benchmark ballots
gave to X, and determine the probability P(X) that X is the
favourite on a ballot drawn randomly from these benchmark ballots.
(I.e., P(X) is the fraction of benchmark ballots favouring X).
Let Z be that option whose total rating is maximal in this group, i.e.
that option Z for which B(Z)B(X) for all X other than Z.
4. For each voter i whose ballot is amoung the deciding ballots, add
the following amount to her voting account C(i):
deltaC(i) := sum { P(X)*( B(X)-T(X,i) ) : X } + T(W,i)-B(Z),
where the sum is over all options X, and where
T(X,i) = T(X)-R(X,i)
is the total rating of X amoung all deciding ballots of voters other
than i.
5. The remaining N-2D voters are the compensating voters. For each
compensating voter j, add the following to her voting accout C(j):
deltaC(j) := - sum { deltaC(i) : i } / (N-2D),
where the sum is over all deciding voters i.
Remarks for version 1:
Since the deciding and benchmark groups are of equal size, the expected
values of T(X) and R(X) are the same, and it is also likely that
Z=W. This implies that the expected value of deltaC(i) given that i
is a deciding voter and all voters report sincere ratings, is just
sum { P(X)*R(X,i) : X } - R(W,i).
In other words, when ratings are sincere a deciding voter can expect to
pay exactly her rating difference between the winner and the Random
Ballot lottery. (This is a major difference to the Clarke tax where this
take Random Ballot as a benchmark philosophy is not incorporated).
Also note that the standard deviation of deltaC(i) under these
assumptions is of an order somewhere between O(sqrt(D)) and O(D),
depending on how correlated the individual voters' ratings are.
Still, the actual price payed by voter i is independent of her ratings
as long as she does not manage to change the winner. Hence there is
still no incentive to bargain for a lower price by misrepresenting my
ratings.
Assuming the true value of W for voter i is U(A,i)=R(W,i), the net
outcome for i is
U(W,i) + deltaC(i)
= sum { P(X)*( B(X)-T(X,i) ) : X } + T(W)-B(Z).
Now assume voter i thinks about changing the winner to A, originally
having a total of T(A)T(W). Since this manipulation does not change
the values T(X,i), the net outcome for i after this manipulation
would be
U(A,i) + sum { P(X)*( B(X)-T(X,i) ) : X } + T(A,i)-B(Z)
= sum { P(X)*( B(X)-T(X,i) ) : X } + T(A)-B(Z).
Since this differs from the first outcome only in that it has T(A)
instead of T(W), it is obviously smaller since T(A)T(W). So after
all, i has no incentive to manipulate the outcome because she would
have to pay more than she gains from this.
Actually, since voter i cannot know who are the deciding, benchmark,
or compensating voters, she cannot base her strategic considerations on
the actual value of W and deltaC(i), but only on their expected
values in the random process of drawing the three voter groups.
The latter observation motivates a second version of the method. In this
version, the winner is determined as before, but the account adjustments
deltaC(i) are averaged over all possible configurations of the three
voter groups. This has the advantage that because of this averaging, the
standard deviation of deltaC(i) will become much smaller than in the
previous versions, and hence the actual value of deltaC(i) will be
quite close to the fair price sum { P(X)*R(X,i) : X } - R(W,i).
Unfortunately, the precise method is a bit technical:
RRVC - New Version 2
0.-2. as above.
3. For each possible partition S of the N voters into disjoint sets
SD,SB,SC of sizes D,D,N-2D, and for each option X,
Re: [Election-Methods] a strategy-free range voting variant?
I performed a quick little simulation for version 2:
With K options and N voters, I drew the all K*N ratings independently
from a standard normal distribution and then applied the method with
D=sqrt(N)/2.
However, instead of using all partitions as suggested, I only used N/2D
partitions. More precisely, I ordered the ballots in a random way in
groups of size D, and then first used groups 1 and 2 as the benchmark
and deciding group, afterwards used groups 3 and 4 for this, then used
groups 5 and 6, and so on. In other words, the account adjustments were
averaged not over all possible partitions but only over these sqrt(N)
many groups.
I did this 100 times for each of a number of different pairs (K,N) and
evaluated the standard deviation of the individual account adjustments.
It turned out that for K=2 this standard deviation was approximately
0.2 / sqrt(sqrt(N))
and only slightly larger for K=16 or K=128.
Since this is quite small when compared to the standard deviation of the
original ratings, which is 1 of course, this averaging in version 2
indeed looks promising! (Without it, the standard deviation of the
individual account adjustments would grow not shrink with growing N.)
Jobst
Jobst Heitzig schrieb:
Dear folks,
this night I had two additional ideas for RRVC, so here's two new
versions of it.
In the first version, the fee F is determined from the benchmark ballots
so that the expected price a deciding voter has to pay from her
voting account is just that voter's rating difference between the winner
and the random ballot lottery:
RRVC - New Version 1
0. Each voter i is assumed to have a voting account whose balance is
denoted C(i).
1. All N voters fill in a range ballot and additionally mark their
favourite in case of a top-rating tie. Voter i can use ratings
0...C(i) only. If C(i) is negative, she can use the rating 0 only
(but still mark her favourite). Let R(X,i) be the rating voter i
gave to option X.
2. Put D = sqrt(N) (rounded up), and draw D deciding ballots. For
each option X, determine the total rating T(X) these deciding
ballots gave to X. The winner W of the decision is that option whose
total rating is maximal, i.e. that option W for which T(W)T(X) for
all X other than W.
3. From the remaining ballots, draw D benchmark ballots. For each
option X, determine the total rating B(X) these benchmark ballots
gave to X, and determine the probability P(X) that X is the
favourite on a ballot drawn randomly from these benchmark ballots.
(I.e., P(X) is the fraction of benchmark ballots favouring X).
Let Z be that option whose total rating is maximal in this group, i.e.
that option Z for which B(Z)B(X) for all X other than Z.
4. For each voter i whose ballot is amoung the deciding ballots, add
the following amount to her voting account C(i):
deltaC(i) := sum { P(X)*( B(X)-T(X,i) ) : X } + T(W,i)-B(Z),
where the sum is over all options X, and where
T(X,i) = T(X)-R(X,i)
is the total rating of X amoung all deciding ballots of voters other
than i.
5. The remaining N-2D voters are the compensating voters. For each
compensating voter j, add the following to her voting accout C(j):
deltaC(j) := - sum { deltaC(i) : i } / (N-2D),
where the sum is over all deciding voters i.
Remarks for version 1:
Since the deciding and benchmark groups are of equal size, the expected
values of T(X) and R(X) are the same, and it is also likely that
Z=W. This implies that the expected value of deltaC(i) given that i
is a deciding voter and all voters report sincere ratings, is just
sum { P(X)*R(X,i) : X } - R(W,i).
In other words, when ratings are sincere a deciding voter can expect to
pay exactly her rating difference between the winner and the Random
Ballot lottery. (This is a major difference to the Clarke tax where this
take Random Ballot as a benchmark philosophy is not incorporated).
Also note that the standard deviation of deltaC(i) under these
assumptions is of an order somewhere between O(sqrt(D)) and O(D),
depending on how correlated the individual voters' ratings are.
Still, the actual price payed by voter i is independent of her ratings
as long as she does not manage to change the winner. Hence there is
still no incentive to bargain for a lower price by misrepresenting my
ratings.
Assuming the true value of W for voter i is U(A,i)=R(W,i), the net
outcome for i is
U(W,i) + deltaC(i)
= sum { P(X)*( B(X)-T(X,i) ) : X } + T(W)-B(Z).
Now assume voter i thinks about changing the winner to A, originally
having a total of T(A)T(W). Since this manipulation does not change
the values T(X,i), the net outcome for i after this manipulation
would be
U(A,i) + sum { P(X)*( B(X)-T(X,i) ) : X } + T(A,i)-B(Z)
= sum { P(X)*( B(X)-T(X,i) ) : X } + T(A)-B(Z).
Since this differs from the
Re: [Election-Methods] delegate cascade
At 07:36 AM 7/21/2008, Kristofer Munsterhjelm wrote: That sounds very much like Delegable Proxy, which Abd says was first thought of by Dodgson (Lewis Carroll). In DP, as far as I understand it, voters associate with proxies (delegates in your terminology) and the proxies accumulate votes from those voters. A proxy is then just like any other voter, and may vote directly or pass the ballot bulk (in sum or part) to yet others. Yes. The idea has been independently invented, how, recently, in a half-dozen or so different places around the world, as far as we know. My guess is there are others we don't know about. Dodgeson's idea was to deal with exhausted ballots in STV by allowing candidates ranked first preference to serve, essentially, as proxies for the voters, so the context was simply an STV election for proportional representation, but that little tweak turns standard STV PR into Asset Voting, and Dodgeson used the same metaphor as Warren Smith, later, in 2004 I think it was. (The candidates can treat the votes as if they were their own property Dodgeson) or their Assets (Smith). A similar idea was called Candidate Proxy, and there are posts to this list or its predecessor, early on, from Mike Ossipoff and I think it was Forest Simmons? My own idea dates back at least twenty years, but, though I talked about it with people, I didn't start publishing until, as I recall at the moment, 2003, I'd have to look at the wayback machine. Dodgeson wrote his comment in 1884. Quite a guy! But the idea is really a no-brainer, once one sits with it long enough and sets aside all the crap that keeps us from seeing new things. It's not really new! It is actually just standard proxy voting with a slight twist, that was always possible but not, previously, necessary (a standard proxy could generally, before, delegate the right involved, and it's common that they do, but more than one level of delegation would be very rare. Standard proxy was solving a different problem, a smaller-scale problem. I don't think that Carroll realized the full implications of his idea. But he did get that this would empower ordinary voters, who, he noted, did not generally have sufficient information to rank umpteen candidates, but who would know whom they most trusted, and that is what he mentions. If you remove the ability of proxies to pass the votes on, and instead let the proxies decide upon the composition of a traditional assembly, you get Asset Voting. However, that doesn't go very well with your continuous election idea, since the assembly presumably has to reside for a given period, just like one that would be directly elected by the voters. Actually, no. If the Asset election creates an electoral college, i.e., a body of public voters whose identities are known, then two things become possible, quite remarkable things, long considered impossible. (1) Recall of members becomes possible, quickly and easily, by those who gave them votes withdrawing those votes. It's easy to overlook this, because we think of an STV election and assume that an Asset one would be the same except for a few details. But Asset makes a major shift: votes are no longer wasted if cast for some relative unknown, say, your uncle Fred who knows more than politics than you and you trust him. I'd predict that, in fairly short order and quite naturally, direct election by secret ballot votes would become rare, people would realize that they could, almost without limitation, vote for the person they most trust, it doesn't have to be a candidate except in a technical sense (the person might have to be registered, and I'd expect there to be a directory of registered candidates available, and it is possible that names would not even be on the ballot, eventually. So while there might be a kind of term, i.e., the period to the next regular election, the composition of the assembly could shift ad interim. My guess is that such assemblies would be relatively stable, though, and I'd also expect rules that ensured lack of serious volatility, and see the next possibility that makes this possible and harmless. (2) Direct democracy of a kind becomes possible! Once there is this body of known, identified, electors, it then becomes possible for them to vote on matters before the assembly. Most of them wouldn't do it, I'd predict, but there would come to be a penumbra of active electors who do vote routinely, or who serve as advisors to those whose seats they created. When an elector votes directly, the value of that vote (which has to do with the original election fraction) is substracted from the vote of the seat. My guess is that normally, these fractional votes would be small enough to not shift results, but the fact that they could do so, and would do so if somehow the Assembly lost the trust of the body of electors (who should not be impeachable except for vote fraud, though some might be
Re: [Election-Methods] [english 97%] Re: [english 80%] CTT voting
Dear Warren and list members, you wrote: The main differences, however, are these: - Voting money is transferred on a regular basis, not only in the very rare case of swing voters, thus making the strategic incentive much stronger. --this is good. However, in one of your revised schemes you made the deciders become a very small fraction of the population instead of (as originally) 1/3. That means very few voters are connected to reality via (your equivalent of) Clarke taxes. I think you have a DILEMMA: A* If you make there be many deciders, then the compensators tend to pay too much money. B* If you make there be too few deciders, then a voter is unlikely to be a decider, and hence her economic incentives to vote honestly, are diminished. B was also a problem with CTT voting - the Clarke payments were rare, divorcing voters from reality. Need to seek the best tradeoff between A B. That could be another reason for using the averaging process of version 2, since it treats all voters alike as potential deciders, so it distributes the incentive evenly. - The transfers are so designed that they compensate those deciding voters who get a worse result than with the random ballot lottery, thus keeping with the philosophy that that lottery is to be considered the benchmark for every more efficient choice. --the random ballot lottery (unfortunately?) is a pretty low benchmark. Low only in terms of efficiency. But the focus is not on efficiency here (that is solved by electing the option maximizing the average rating) but on equality and fairness. In my opinion, every voters has a priori a right to distribute a share of 1/N of the winning probability. So if a method takes away this control, it has to compensate the voter. (You might remember that we had this benchmark discussion already about a year ago... :-) You could also consider the random candidate lottery (elect each with probability 1/K, where K candidates in all). That is an even-worse benchmark than random ballot, but it is simpler and does not depend on the votes at all. Because it does not depend on votes, you then would not need your benchmarker class of voters, only deciders and compensators. See above for the motivation why it is exactly the Random Ballot process which has to serve as the benchmark in my view. Also, a random candidate lottery is not clone-proof. - Voting money is not destroyed and then gradually refilled but is always preserved, thus keeping its value constant. --Is there a worry that over a sequence of elections, we get unfairness? That might occurr if the variance of the adjustments is too large, so that it could happen that only by sheer bad luck a voter's account becomes negative and the voters cannot influence the next decision until her account is positive again. Also for this reason the variance of the adjustments due to the random assignment of groups should be as small as possible. In election #1, suppose you are correct and so everybody wants to vote honestly. Excellent. BUT now in election #2, some voters have more money than others, hence have more power. COULD IT HAPPEN THAT this inequality could be CORRELATED with the politics? If so, then in election #2, the Democrats would win, unfairly, purely because Democrats have more power. If this could somehow feed back (so that in election #3, democrats also tended to have more money, and so on forever) this could be extremely bad. Hmm... I hope the feedback will always be negative, partly because the benchmark against which compensations are determined is not the majority choice but the average choice (Random Ballot). Also, your benchmarkers could have motivation to vote DIShonestly, thus defeating the purpose. CONCRETE SCENARIO TO WORRY ABOUT: The benchmarker votes affect the payouts. If benchmarkers dishonestly rank the Democrat top, that tends to cause those who rate Democrats low, to get lower payoffs. That causes Democrats to have more money in election #2. That causes this strategy to work even better in election #2. Feedback. Disaster. (I'm not sure whether this scenario is a real problem. But it might be.) A REPAIR: Note that in the random-candidate-lottery there are no benchmarkers, hence the worry I just described perhaps no longer exists. -wds Let us think about this some further. My hope is that because (i) a voter does not know whether she is a benchmark voter, and (ii) the benchmark group will usually be a representative sample of the electorate, and (iii) the averaging process of version 2 treats all voters alike when it comes to adjustments, the incentive described by you will be averaged out if it exists in the first place. But surely this deserves more detailed research... Yours, Jobst Election-Methods mailing list - see http://electorama.com/em for list info
Re: [Election-Methods] delegate cascade
Hi, Some more comments and questions on the properties of the proposed method. 1) All voters are candidates and it is possible that all voters consider themselves to be the best candidate. Therefore the method may start from all candidates having one vote each (their own vote). Maybe only after some candidates have numerous votes and the voter himself has only one vote still, then the voter gives up voting for himself and gives his vote to some of the frontrunners. How do you expect the method to behave from this point of view? 2) Let's say that the preferences of voter A are ABCDE. At some point he decides to vote for his second preference (B) instead of himself. B's preferences are BDetc. At some (later) point B decides to vote for his second preference D. A is however not happy with that the vote now goes directly to D (instead of C that was better). He changes his vote and votes for C. The point here is that it may be that many voters will vote directly the leading candidates instead of letting the voters in longer chains (according to their own preferences) determine where the vote ends at. The reason may be as above or maybe the voter simply prefers to vote directly for the leading/best candidates instead of being at the long branches of the tree (away from the main streams close to the root of the trees where the decision making appears to take place). Controlling one's own vote may also give the voter some additional negotiating power. The end result may be that the cascade chains may tend to be short rather than long. The same question here. Is this ok and how do you expect the method to behave? 3) In theory the method may also end up in a loop. There could be three voters (A, B, C) with opinions A: ABC, B: BCA and C: CAB. If A votes for A, B votes for B and C votes for A, then B has an incentive to change his vote to C in the hope that also C will vote for himself after this move. That would improve the result from B's (as well as C's) point of view (from A to C). But as a result now A has a similar incentive to vote for B that is to him better than C. And the story might continue forever. This kind of loops would probably be rare. But do you think this is acceptable or should there be some limitations that would eliminate or slow down possible continuous changes in the votes? In this looped case is possible that when the voters note the loop they are capable of negotiating some compromise solution (e.g. A and C agree that C will get something in return if he sticks to voting for A). Juho Laatu On Jul 21, 2008, at 14:36 , Kristofer Munsterhjelm wrote: Michael Allan wrote: Hello to the list, Hello, and welcome. 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? That sounds very much like Delegable Proxy, which Abd says was first thought of by Dodgson (Lewis Carroll). In DP, as far as I understand it, voters associate with proxies (delegates in your terminology) and the proxies accumulate votes from those voters. A proxy is then just like any other voter, and may vote directly or pass the ballot bulk (in sum or part) to yet others. If you remove the ability of proxies to pass the votes on, and instead let the proxies decide upon the composition of a traditional assembly, you get Asset Voting. However, that doesn't go very well with your continuous election idea, since the assembly presumably has to reside for a given period, just like one that would be directly elected by the voters. There's also the council democracy system that, I think, is used in some unions. There you have local councils that elect among their number to regional councils that
