Re: [EM] Some chance for consensus revisited: Most simple solution
Hi Raph, The odds of it actually working are pretty low. For it to work, all voters must be aware that C is a valid compromise. Sure, that's the flipside of it being so ultimately simple. The easiest way to safeguard against a small number of non-cooperative voters would be to require only, say, 90% of the consensus ballots to have the same option ticked in order for that option to be elected. I guess that's what you mean by threshold: In practice, there needs to be a reasonable threshold. There is always going to be a need to balance tyranny of the (N%) majority against the hold-out problem. Even with a 90% threshold, a tyranny of a 90% majority can be avoided, but this requires another slight modification: Instead of on two separate ballots, every voter marks her favourite and consensus options on one ballot using markers 1 and 2. Then a ballot is drawn at random. If at least 90% of all ballots mark the same option 2 as this drawn ballot does, then that option wins. Otherwise the option marked 1 on the drawn ballot wins. In this way, a bullet-voting faction of, say, 5%, allocates at least 5% winning probability to their favourite (as required by my interpretation of democratic method). Yours, Jobst Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Some chance for consensus revisited: Most simple solution
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
Re: [EM] Some chance for consensus revisited: Most simple solution
You're absolutely right, Juho -- I modified the condition a number of times and didn't realize the last version did not imply both factions prefer C to Random Ballot. The correct set of situations for which SEC is a solution is characterized by both factions prefering C to Random Ballot. The latter is in particular true when alpha=beta and C has the largest total utility. Sorry for the mistake, Jobst Juho Laatu schrieb: Makes sense but doesn't this allow also 50: A(100) C(40) B(0) 50: B(100) C(70) A(0) where 50*40 + 50*70 max(50,50)*100 but the A supporters may prefer random ballot from the favourites urn to the possible consensus result (C) and therefore vote (e.g.) for A in their consensus ballot. Juho --- On Sun, 1/2/09, Jobst Heitzig heitzi...@web.de wrote: From: Jobst Heitzig heitzi...@web.de Subject: [EM] Some chance for consensus revisited: Most simple solution To: election-methods@lists.electorama.com Date: Sunday, 1 February, 2009, 11:02 PM 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
