Re: [EM] Current SODA not monotonic; fixable. (mono-voter-raise)
Responding to Abd: Asset is a great system. But it is far from perfect. Unlike SODA, it is far from resolvable. This can lead to center squeeze worse than IRV's (in fact, so bad that I'm tempted to Godwin it), or even, in principle, a chicken dilemma. In fact, in a sense, all parliamentary systems are flawed proto-Asset systems; and there are valid reasons to dislike parliamentary systems, as for instance I'd say the collapse of the Lib Dems shows. These are all flaws which SODA fixes. Both Asset and SODA have its place; you might call SODA a fish bicycle but of course bicycles are quite useful for some non-fishes. As for the non-monotonic example: B has a preference order but for whatever reason got no delegated votes so it's irrelevant. Trying to build a plausible story around this scenario, which I estimate will happen around 1 in 6⁷=280,000 4-candidate elections, is a waste of time. (I'm programming a monte-carlo simulation which should give a more accurate number there. For more candidates, this probability will rise, but it would still take around 50 *viable* candidates to make the scenario actually likely). 2013/4/20 Abd ul-Rahman Lomax a...@lomaxdesign.com At 01:09 PM 4/19/2013, Jameson Quinn wrote: Consider the following scenario in SODA: 1: A(CBD) 2: B,X 2: C(BAD) 1: D(ACB) 1: null Presume all ties are predictably broken for the alphabetically-first candidate (without this presumption, you'd need larger numbers, but you could still make a similar scenario). Under SODA with rational delegation assignment, C has a choice. If C does not approve B, they are giving A and D a choice between approving A and C so C wins, or only A so A wins; since both A and D will choose the latter, this is tantamount to electing A. If C does approve B, then B will win regardless of what A and D do. C prefers B, so B wins. Notice that SODA is, generally, an Asset Method, but, first of all, heavily restricted. It loses the most appealing and probably the most useful aspect of Asset, the creation of a *deliberative* body that can resolve an election. Instead, because of the rules, the votes of canididates are *predictable*, within the restrictions, and thus C is able to, in the scenario given, know how the others will vote, and to use that information for personal advantage. The vote that is allegedly non-monotonic is an odd one, and I've made this point about Asset many times: why would one vote for a candidate, who presumably will represent the voter in hundreds or thousands of decisions, if elected, but not trust that candidate to delegate? Which is what real representatives and executives do, a great deal of the time. Not having the skill and understanding to delegate rationally is a major shortcoming in any person heavily participating in executive or governmental decisions. Making poor choice in delegation has led to the downfall of many. But if the last null voter adds an undelegated approval for B, then if C approves nobody and D and A approve only A, the result shifts from A to B. Since C knows that A and D will prefer to give the win to C, now C can safely not approve B, and win. Essentially, the lone voter makes the world safe for C. B has apparently also not indicated delegations. Perhaps that's why the null voter didn't allow delegation. The *system* defanged B. C essentially betrays B (though we have no clue as to the depth of that betrayal, and since B did not declare delegations, we also don't know how B would have voted in the further process.) I've generally written that without knowing underlying utilities, we cannot understand the impact of a criterion failure. However, we can guess that the preference strength of the null voter for B over the others is weak. I don't know if the rules would have allowed B to vote the null voter's ballot if the vote had been delegable, given a lack of prestated delegations. SODA is *not* simple, as the name claims. Asset is simple, and we suggested, years, ago, FAAV, fractional approval asset voting, which would *allow* voters to vote for more than one, with the vote being divided if needed for completion. Most voters would presumaby vote for one only. So the ballot is a pure approval ballot, and there is *only one question* the voters need to address: whom do you trust most to represent you in the ensuing process? And such a vote is clearly monotonic, in itself. That is, it always increases the voting power of the candidate(s) voted for. However, in real life, in real decisions, it can occur in the process that an increase in power of a faction shifts the process in a way that ultimately is against the interest of that faction. That's a *basic problem*, not a voting system problem. It's rare, but simply not impossible. The most common situation would be overreach. I.e., a faction might have a position that will prevail, but if, believing that they have the power, they disregard and reject
Re: [EM] Current SODA not monotonic; fixable. (mono-voter-raise)
On 4/19/2013 11:51 AM, Jameson Quinn wrote: ... Aside from my research paper, which is still progressing, I will soon be publishing a note about SODA and MODA on ArXiv, in which I prove MODA's compliances. Once my research paper, which will reference that note, is peer-reviewed, I hope that will be enough to add MODA to http://en.wikipedia.org/wiki/Voting_system#Compliance_of_selected_systems_.28table.29. It will join MJ and Ranked Pairs among the overall most-compliant systems in that table. One possibility is that MODA might need to be a footnote that clarifies a specific criterion for the SODA entry. I might be wrong. (I haven't analyzed SODA/MODA carefully.) I'm just thinking that MODA is really the SODA method with an escape lever. Whether or not someone pulls the escape lever to get better compliance is not part of the MODA method itself, right? Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Current SODA not monotonic; fixable. (mono-voter-raise)
At 01:09 PM 4/19/2013, Jameson Quinn wrote: Consider the following scenario in SODA: 1: A(CBD) 2: B,X 2: C(BAD) 1: D(ACB) 1: null Presume all ties are predictably broken for the alphabetically-first candidate (without this presumption, you'd need larger numbers, but you could still make a similar scenario). Under SODA with rational delegation assignment, C has a choice. If C does not approve B, they are giving A and D a choice between approving A and C so C wins, or only A so A wins; since both A and D will choose the latter, this is tantamount to electing A. If C does approve B, then B will win regardless of what A and D do. C prefers B, so B wins. Notice that SODA is, generally, an Asset Method, but, first of all, heavily restricted. It loses the most appealing and probably the most useful aspect of Asset, the creation of a *deliberative* body that can resolve an election. Instead, because of the rules, the votes of canididates are *predictable*, within the restrictions, and thus C is able to, in the scenario given, know how the others will vote, and to use that information for personal advantage. The vote that is allegedly non-monotonic is an odd one, and I've made this point about Asset many times: why would one vote for a candidate, who presumably will represent the voter in hundreds or thousands of decisions, if elected, but not trust that candidate to delegate? Which is what real representatives and executives do, a great deal of the time. Not having the skill and understanding to delegate rationally is a major shortcoming in any person heavily participating in executive or governmental decisions. Making poor choice in delegation has led to the downfall of many. But if the last null voter adds an undelegated approval for B, then if C approves nobody and D and A approve only A, the result shifts from A to B. Since C knows that A and D will prefer to give the win to C, now C can safely not approve B, and win. Essentially, the lone voter makes the world safe for C. B has apparently also not indicated delegations. Perhaps that's why the null voter didn't allow delegation. The *system* defanged B. C essentially betrays B (though we have no clue as to the depth of that betrayal, and since B did not declare delegations, we also don't know how B would have voted in the further process.) I've generally written that without knowing underlying utilities, we cannot understand the impact of a criterion failure. However, we can guess that the preference strength of the null voter for B over the others is weak. I don't know if the rules would have allowed B to vote the null voter's ballot if the vote had been delegable, given a lack of prestated delegations. SODA is *not* simple, as the name claims. Asset is simple, and we suggested, years, ago, FAAV, fractional approval asset voting, which would *allow* voters to vote for more than one, with the vote being divided if needed for completion. Most voters would presumaby vote for one only. So the ballot is a pure approval ballot, and there is *only one question* the voters need to address: whom do you trust most to represent you in the ensuing process? And such a vote is clearly monotonic, in itself. That is, it always increases the voting power of the candidate(s) voted for. However, in real life, in real decisions, it can occur in the process that an increase in power of a faction shifts the process in a way that ultimately is against the interest of that faction. That's a *basic problem*, not a voting system problem. It's rare, but simply not impossible. The most common situation would be overreach. I.e., a faction might have a position that will prevail, but if, believing that they have the power, they disregard and reject whatever compromises might be needed to complete implementation, they might eventually lose out. We see that excess power has defeated many movements, i.e., *too much success*. So then they act arrogantly, and create a counterrevolution or strengthen it. So an extra approval for B caused B to lose. So what happened? To review it: 1: A(CBD) 2: B,X 2: C(BAD) 1: D(ACB) 1: null Realize that the process described doesn't happen in the ballots. The voter voting for B gives B additional power in the process, just not enough to prevail without the cooperation of another. 1 vote short, in fact. I'd claim that the *voting* system was monotonic, but the additional vote shifted strategic considerations on the part of C. And SODA sets up pure, full-information strategic voting, and that is a major flaw. Without that extra B vote, the results are, without delegation, A: 1 B: 2 C: 2 D: 1 There are six voters (unless the null voter does count by having cast some ballot, perhaps with a write-in). Majority is 4. C can complete the election for B. Does C do so? Maybe. The assumption here is that C would, but that is an assumption based on no other votes being present.
[EM] Current SODA not monotonic; fixable. (mono-voter-raise)
Consider the following scenario in SODA: 1: A(CBD) 2: B,X 2: C(BAD) 1: D(ACB) 1: null Presume all ties are predictably broken for the alphabetically-first candidate (without this presumption, you'd need larger numbers, but you could still make a similar scenario). Under SODA with rational delegation assignment, C has a choice. If C does not approve B, they are giving A and D a choice between approving A and C so C wins, or only A so A wins; since both A and D will choose the latter, this is tantamount to electing A. If C does approve B, then B will win regardless of what A and D do. C prefers B, so B wins. But if the last null voter adds an undelegated approval for B, then if C approves nobody and D and A approve only A, the result shifts from A to B. Since C knows that A and D will prefer to give the win to C, now C can safely not approve B, and win. So an extra approval for B caused B to lose. Now, even with this flaw, SODA is still a very good system. I've built dozens of voting scenarios in my time, and I can't remember ever building one that took me this much work to get it working the way I wanted. (Note that among its many carefully-balanced aspects, it includes a Condorcet cycle CBAC.) I honestly believe this scenario would never arise. For practical purposes, SODA is indeed monotonic. Still, the lack of bulletproof monotonicity puts a serious damper on SODA's criteria compliances. If I had mono-voter-raise, I could prove the rest of monotonicity, then FBC, a doubly-strong delegated equilibrium for a majority Condorcet winner (which makes it usually rational to delegate), and voted Condorcet, and mutual majority, and probably some others. Without mono-voter-raise, all those proofs fall apart. So I'm considering fixing SODA. The fix that's necessary is to allow candidates to commit to forego some of their votes in the final count. In other words, B here could simply say we won't count that extra approval. With this fix, I can prove monotonicity; and, as I said, the situation would arise once in a purple moon. So, what do people think? Should I change the default definition of SODA to make it have better compliances? Or should I keep it the way it is because the change would never matter in practical terms and would only make the system sound more complex? Sincerely, Jameson Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Current SODA not monotonic; fixable. (mono-voter-raise)
On 4/19/2013 11:09 AM, Jameson Quinn wrote: ... So, what do people think? Should I change the default definition of SODA to make it have better compliances? Or should I keep it the way it is because the change would never matter in practical terms and would only make the system sound more complex? Join the club. Each of us favors a method that fails some criterion or another. I think the best fix is to identify how often each failed criterion occurs. Probably as a percentage, or a percentage range. Of course that's difficult to do. Yet it will be more meaningful than just having a yes-or-no checkbox for each criterion. Keep in mind that if you create a variation of SODA, that amounts to creating a new method, which probably requires a new name (or a qualification added to the SODA name). Of course this reply doesn't directly answer your question. The best solutions are not necessarily easy, but usually they are simple. Richard Fobes Election-Methods mailing list - see http://electorama.com/em for list info
