Dear folks, I want to describe the most simple solution to the problem of how to make sure option C is elected in the following situation:
a% having true utilities A(100) > C(alpha) > B(0), b% having true utilities B(100) > C(beta) > A(0). with a+b=100 and a*alpha + b*beta > max(a,b)*100. (The latter condition means C has the largest total utility.) The ultimately most simple solution to this problem seems to be this method: Simple Efficient Consensus (SEC): ================================= 1. Each voter casts two plurality-style ballots: A "consensus ballot" which she puts into the "consensus urn", and a "favourite ballot" put into the "favourites urn". 2. If all ballots in the "consensus urn" have the same option ticked, that option wins. 3. Otherwise, a ballot drawn at random from the "favourites urn" decides. Please share your thoughts on this! Yours, Jobst Jobst Heitzig schrieb: > Hello folks, > > I know I have to write another concise exposition to the recent > non-deterministic methods I promote, in particular FAWRB and D2MAC. > > Let me do this from another angle than before: from the angly of > reaching consensus. We will see how chance processes can > help overcome the flaws of consensus decision making. > > I will sketch a number of methods, give some pros and cons, starting > with consensus decision making. > > Contents: > 1. Consensus decision making > 2. Consensus or Random Ballot > 3. Approved-by-all or Random Ballot > 4. Favourite or Approval Winner Random Ballot: 2-ballot-FAWRB > 5. Calibrated FAWRB > 6. 4-slot-FAWRB > 7. 5-slot-FAWRB > > > > 1. Consensus decision making > ---------------------------- > The group gathers together and tries to find an option which everyone > can agree with. If they fail (within some given timeframe, say), the > status quo option prevails. > > Pros: Ideally, this method takes everybody's preferences into account, > whether the person is in a majority or a minority. > > Cons: (a) In practice, those who favour the status quo have 100% power > since they can simply block any consensus. (b) Also, there are problems > with different degrees of eloquence and with all kinds of group-think. > (c) Finally, the method is time-consuming, and hardly applicable in > large groups or when secrecy is desired. > > > Let us address problem (a) first by replacing the status quo with a > Random Ballot lottery: > > > 2. Consensus or Random Ballot > ----------------------------- > Everybody writes her favourite option on a ballot and gives it into an > urn. The ballots are counted and put back into the urn. The number of > ballots for each option is written onto a board. The group then tries to > find an option which everyone can agree with. If they fail within some > given timeframe, one ballot is drawn at random from the urn and the > option on that ballot wins. > > Pros: Since the status quo has no longer a special meanining in the > process, its supporters cannot get it by simply blocking any consensus - > they would only get the Random Ballot result then. If there is exactly > one compromise which everybody likes better than the Random Ballot > lottery, they will all agree to that option and thus reach a good > consensus. > > Cons: Problems (b) and (c) from above remain. (d) Moreover, it is not > clear whether the group will reach a consensus when there are more than > one compromise options which everybody likes better than the Random > Ballot lottery. (e) A single voter can still block the consensus, so the > method is not very stable yet. > > > Next, we will address issues (b), (c) and (d) by introducing an approval > component: > > > 3. Approved-by-all or Random Ballot > ----------------------------------- > Each voter marks one option as "favourite" and any number of options as > "also approved" on her ballot. If some option is marked either favourite > or also approved on all ballots, that option is considered the > "consensus" and wins. Otherwise, one ballot is drawn at random and the > option marked "favourite" on that ballot wins. > > Pros: This is quick, secret, scales well, and reduces problems related > to group-think. A voter has still full control over an equal share of > the winning probability by bullet-voting (=not mark any options as "also > approved"). > > Cons: (b') Because of group-think, some voters might abstain from using > their bullet-vote power and "also approve" of options they consider > well-supported even when they personally don't like them better than the > Random Ballot lottery. Also, (e) from above remains a problem, in > particular it is not very likely in larger groups that some options is > really approved by everyone. > > > Now comes the hardest part: Solving problems (b') and (e) by no longer > requiring full approval in order to make it possible to reach "almost > unanimous consensus" when full consensus is not possible. In doing so, > we must make sure not to give a subgroup of the electorate full power, > so that they can simply overrule the rest. Instead, we must make the > modification so that still every voter has full control over an equal > share of the winning probability. This is why we cannot just lower the > threshold for consensus from 100% to, say, 90%. What we do instead is this: > > > 4. Favourite or Approval Winner Random Ballot (FAWRB), > simplest version, using two ballots (2-ballot-FAWRB) > ------------------------------------------------------- > Still, each voter marks one option as "favourite" and any number of > options as "also approved" on her ballot. The option getting the largest > number of "favourite" or "also approved" marks is nominated as > "compromise". Two ballots are drawn at random. If the nominated > compromise is marked on both as "favourite" or "also approved", it wins. > Otherwise, the option marked as "favourite" on the first of the two > ballots wins. > > Pros: Full consensus can be reached if some option is approved by > everyone. Such an option will win with certainty. If no such option > exists, also partial consensus can be reached: if, say, 90% agree to the > best compromise option, that option will win with at least 81% > probability (=90%*90%). On the other hand, bullet-voting still assures > that my favourite gets my share of the winning probability: if 5% > bullet-vote, their favourite gets at least 5% of the winning > probability. Problem (b') shall no longer exist since by not approving I > do not destroy the consensus complete but only lower the compromise's > probability a bit. > > Cons: (f) The incentive to approve a good compromise is only there when > I prefer the compromise quite a lot to the Random Ballot lottery, not > when I prefer it only slighty. (g) If the process of nominating options > does not prevent this, there is the possibility that a really harmful > option is elected with some small probability. > > > (Another method which achieves almost the same as 2-ballot-FAWRB is the > older D2MAC which is very similar.) > > > The game-theoretic reason for problem (f) is this: > > Consider a situation in which C is the compromise and all N voters > approve it (N being large for simplicity). Now consider that I ask > myself whether it would server my better not to approve C but to > bullet-voter for my favourite, A. If I remove my approval for C, the > winning probabilities change in the following way: C no longer wins with > probability 1 but only with approximately probability 1 - 2/N (more > precisely 1 - 2/N + 1/N²). My favourite A's winning probability grows > from 0 to 1/N, since A now wins whenever my ballot is the first of > the two drawn ballots. But at the same time, also the other voters' > favourites' winning probabilities grow, since another voter's favourite > now wins when my ballot is the second drawn ballot. In other words, the > probability of ending up with a Random Ballot lottery result grows from > 0 to approximately 1/N, too. Therefore, bullet-voting only makes > sense when the utility I assign to the compromise C is smaller than the > mean of (i) the utility I assign to my favourite A and (ii) the utility > I assign to a Random Ballot lottery. In other words, it is better to > cooperate in the election of C only when I rate C higher than half the > way up from my rating of the Random Ballot lottery to my favourite's > rating. > > > Important: Although the FAWRB process always uses a chance process, > namely drawing ballots, it will still usually lead to a deterministic or > almost deterministic result! This is because with the incentives in > place, people are usually very good at finding compromises which they > then will (almost) all approve of, giving them 100% (or almost 100%) > winning probability! Just as in "Consensus or Random Ballot", the very > fact that the voters don't like the Random Ballot lottery when a > compromise exists will lead to the compromise being elected and the > Random Ballot being avoided. > > > The next step towards my recommended version of FAWRB reduces this > problem (f) by replacing the fixed number of three ballots by a more > sophisticated drawing process: > > > 5. Favourite or Approval Winner Random Ballot, > calibrated version, using 3 or 15 ballots (calibrated FAWRB) > --------------------------------------------------------------- > Still, each voter marks one option as "favourite" and any number of > options as "also approved" on her ballot. The option getting the largest > number of "favourite" or "also approved" marks is still nominated as > "compromise". A die is tossed. If it shows a six then 15 ballots are > drawn at random, otherwise only 3 ballots. If the nominated compromise > is marked on all these ballots as "favourite" or "also approved", it > wins. Otherwise, the option marked as "favourite" on the first of the > drawn ballots wins. > > Pros: As in 2-ballot-FAWRB, but now voters will also approve compromises > they only find slightly better than the Random Ballot lottery (more > precisely: which they rate higher than 1/5 of the way up from their > rating of the Random Ballot lottery to their favourite's rating). > > Cons: Problem (g) from above remains. (h) When there are more than one > possible compromise options, say C1 and C2, some voters may apply > "approval strategy" and refuse to approve of C1 in order to get C2 > nominated instead of C1. When C1 is nominated anyway, they thereby > reduce C1's winning probability unnecessarily. > > > Mathematical note: The reason why the mentioned "approval limit" moves > from 1/2 down to 1/5 of the way from Random Ballot to favourite is that > the expected number of ballots drawn moved from 2 to 5. > > > Next, we tackle problem (h) by decoupling the nomination of the > compromise from the later agreement to the nominated compromise. This > can be achieved by simply splitting the "also approved" slot into two > slots named "good compromise" (used for both nomination and agreement) > and "agreeable" (used only for agreement): > > > 6. Favourite or Approval Winner Random Ballot, > version with four slots (4-slot-FAWRB) > ---------------------------------------------- > Each voter marks one option as "favourite", any number of options as > "good compromise" and any number of options as "agreeable" on her > ballot, the unmarked options being implicitly regarded as "bad". The > option getting the largest number of "favourite" or "good compromise" > marks (but not counting "agreeable" marks!) is nominated as > "compromise". A die is tossed. If it shows a six then 15 ballots are > drawn at random, otherwise only 3 ballots. If the nominated compromise > is marked on all these ballots as "favourite", "good compromise", or > "agreeable", it wins. Otherwise, the option marked as "favourite" on the > first of the drawn ballots wins. > > Pros: Voters can now use approval strategy for the nomination step > without reducing the final winning probability of the nominated > compromise: The can just give only some one of the potential compromise > options the "good compromise" mark and giving the other acceptavle > compromise options the "agreeable" mark. > > Cons: Only problem (g) might remain. > > > The final step is only needed when there is the possibility that some > really bad option can actually make it onto the ballot. It is not needed > when options are first checked by some independent authority for their > feasibility, as is often implicitly done in political systems by supreme > courts or the like. > > So, if (g) is really a problem, we can try to reduce it by introducing > some mechanism by which a really large majority (say, 90%) can > prevent an option from being accepted on the ballot. This leads me to > the final version of FAWRB: > > > 7. Favourite or Approval Winner Random Ballot, > version with supermajority-veto (5-slot-FAWRB) > ------------------------------------------------- > Each voter marks one option as "favourite", any number of options as > "good compromise", any number of options as "agreeable", and maybe some > options as "harmful" on her ballot, the unmarked options being > implicitly regarded as "bad". Every option receiving more than 90% > "harmful" marks is removed before we continue as in 4-slot-FAWRB: Of the > remaining options, the one getting the largest number of "favourite" or > "good compromise" marks (but not counting "agreeable" marks!) is > nominated as "compromise". A die is tossed. If it shows a six then 15 > ballots are drawn at random, otherwise only 3 ballots. If the nominated > compromise is marked on all these ballots as "favourite", "good > compromise", or "agreeable", it wins. Otherwise, the option marked as > "favourite" on the first of the drawn ballots wins. > > Pros: The "harmful" slot allows a 90% majority to keep harmful extremist > options from having a chance. > > Cons: This supermajority-veto can be used to oppress minorities which > are smaller than 10%, because they have no longer full control over > their share of the winning probability. > > > Hopefully that explains some things. > I will also put the definitions into the Electowiki within a few days. > > Yours, Jobst > > > Raph Frank schrieb: >> On Sat, Oct 25, 2008 at 8:02 PM, Greg Nisbet >> <[email protected]> wrote: >>> Ok now the actual criticism. I know that FAWRB is nondeterministic. >>> Here is why that is bad. >>> >>> Factions (both unwilling to compromise): >>> >>> A 55% >>> B 45% >>> >>> you view A as gaining a "55% chance of victory". >>> >>> This reasoning is flawed. Instead of viewing A as getting .55 victory >>> units, think of it as a random choice between two possible worlds: >>> >>> A-world and B-world >>> >>> A-world is 10% more likely to occur, however they share remarkable >>> similarities. >>> >>> In both worlds >=45% of the people had no say whatsoever. >> >> The trick with his method is that neither A-world or B-world is likely >> to actually occur. It creates an incentive to find a compromise, >> called say, AB-world. >> >> If all voters vote reasonably, then the result is a high probability >> that the AB option will be picked. >> >> The utlities might be >> ..... A-AB-B >> 55: 100-70-0 >> 45: 0-70-100 >> >> In effect, each A supporter agrees to switch his probability to AB in >> exchange for a B supporter switching to AB. >> >> So, the initial probabilities would be >> >> A: 55% >> AB: 0% >> B: 45% >> >> Expected utility >> 55: 55 >> 45: 45 >> Total: 100 >> >> However, after the negotiation stage, the results might be >> >> A: 10% >> AB: 90% >> B: 0% >> >> Expected utility >> >> 55: 10% of 100 and 90% of 70 = 73 >> 45: 90% of 70 = 63 >> Total: 136 >> >> I don't 100% remember the method (and it could do with a web >> description :p ), but that is what it is attempting to do. >> >> The idea is not that it is random. The idea is that it says "OK, if >> you can't all agree on a compromise, then we will pick a winner at >> random". >> >> The threat that a random winner will be picked is what allows the >> negotiation. If a majority can just impose its will, then there is no >> point in compromising. > > ---- > Election-Methods mailing list - see http://electorama.com/em for list info ---- Election-Methods mailing list - see http://electorama.com/em for list info
