[EM] Current SODA not monotonic; fixable. (mono-voter-raise)

[Jameson Quinn]

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 <abd at lomaxdesign.com>

> At 01:09 PM 4/19/2013, Jameson Quinn wrote:
>
>> Consider the following scenario in SODA:
>>
>> 1: A(>C>B>D)
>> 2: B,X
>> 2: C(>B>A>D)
>> 1: D(>A>C>B)
>> 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(>C>B>D)
> 2: B,X
> 2: C(>B>A>D)
> 1: D(>A>C>B)
> 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. C is
> presumaby concerned about the election of A or D. Yet if B cannot delegate
> votes, by the rules, and C stands pat, the election fails to find a
> majority. And I found the SODA rules unclear on that. Using an Asset type
> method without requiring a majority is asking for trouble.... this
> collection of candidates *can* find a majority, and if they don't, it's due
> largely to C, who *would* be blamed for it. I'd agree. C would be *likely*
> to approve B; however, the monotonicity criterion is not interpreted with
> "maybe"s.
>
> C *must* approve B or none, as I read the SODA rules. If C approves none,
> and if the other candidates imitate Bucklin, the election goes to
>
> A: 2
> B: 2
> C: 3
> D: 1
>
> then to
>
> A: 3
> B: 3
> C: 4
> D: 2
>
> C wins. The conclusion that C must approve B is weak, very weak. Using the
> fourth preference votes is highly questionable. Last preference is
> considered an approval?
>
> Asset methods cannot be analyzed using classical voting systems criteria,
> in general, because the subsequent voting is *free*. It is really a further
> process, and the effect of the voting in the public election is to create
> and empower participants in that further process.
>
> However, the special rules of SODA, which are, to my mind, a nightmare,
> prevent that from working. If this were *not* optional delegation, and if a
> majority is required to complete -- both of which I highly recommend for
> Asset elections, we do *not* place the legislature under a gun requiring
> them to complete a decision by any particular time -- what would happen? We
> don't do that with deliberative bodies, period, except for *natural
> consequences*. I.e., if the country goes to hell in a handbasket because of
> the legislator's dawdling and refusing to compromise, it goes there and
> then we *blame them* for it. And election somebody else. But that only
> occurs, in my experience, when we have created strong factions and have
> balanced them, in how we vote, and Asset systems make party affiliation
> *unnecessary* to gain a level of power. That's because Asset doesn't waste
> votes. Above, we see the problem of wasted votes.
>
> So with pure delegation, no restriction on revoting, we start out, given
> that extra vote, with
>
> A: 1
> B: 3
> C: 2
> D: 1
>
> Majority is 4. Now, if B holds out, B's name is *mud*, assuming that the C
> voters have the same preferences as C. We already know, from the stated
> preferences, that B is the legitimate winner, by most assumptions. If C
> holds out, C will lose clout, influence with B. B may negotiate with A, the
> most likely source of the additional vote other than C. A has a chance here
> to negotiate some real power -- set up by C's intransigence.
>
> It's unlikly. C would just approve B and then move on.
>
> Single-winner elections by public ballot plurality are essentially
> *obsolete*. It was a compromise made because it was believed to be
> necessary. It's not necessary.
>
> The entire Asset concept can be used to reduce *any decision* to a process
> that involves a decreased number of participants, and for the public part
> of this (i.e., what the "public voters" do, those holding the Assets), it
> can be boiled down quickly to whatever size committee is necessary to make
> recommendations, all, again, through trusted representatives. Single-winner
> makes *no sense* for representation, even when elected by a majority. What,
> is the minority not to be represented at all? That disempowers up to half
> the population! Why?
>
> (Single-representation made sense when we thought in terms of a "district"
> or "population" being represented, and when it was assumed that, really,
> what was being selected was *character*, and there was a belief that
> representatives would faithfully represent *the whole population.* Many
> still attempt to do that, but ... the result is a major distance created
> between people and the government. Alienation.)
>
> So, while Asset does work for single-winner, it's like using a computer as
> a hammer. No, the place to push for Asset is in the election of
> representative bodies, and I'd go for full-out, virtual-district -- i.e.,
> no district except as the voters and electors naturally distinguish
> themselves by district -- and when this is done, the Assembly becomes
> accurately proportional by whatever standard is used, assuming that people
> vote according to the standard. And if the people want something different
> -- like, say, all women -- they could create that. But, in fact, what they
> create will be *unpredictable,* except that we can predict that the
> Assembly will accurately represent the people, in whatever process ensues,
> and the communication between the Assembly and the people will be
> *excellent.* The full electoral college creates the link.
>
>
>  Now, even with this flaw, SODA is still a very good system.
>>
>
> It adds complications to simple Asset that create, then, the scenario
> described. Given how simple Asset can be, as to ballot, given how simple it
> is to handle "overvoting" with fractional assignments, I'd leave it at that.
>
>
>   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 C>B>A>C.) I honestly believe this scenario would never
>> arise. For practical purposes, SODA is indeed monotonic.
>>
>
> It's possible to assert that it is still monotonic in the scenario
> described; that is, the lone voter gave only a very limited power to B. And
> the application of the monotonicity criterion to *subsequent deliberative
> process* is outside its design intention.
>
>  [...]
>>
>>
>> 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?
>>
>
> I think you are working on the excruciating details of a fish bicycle.
>
> Remember, we had an Asset election. It was a vote-for-one, the voting
> method, on-line, locked out overvotes. The system was inadequately
> specified, but the basic Asset concept is so powerful that it didn't
> matter. Essentially, the electors worked it out. We actually disregarded
> what had been stated as the rules. And deliberative bodies can normally do
> that! We did this, collectively, as a smaller subset of the electorate who
> had been empowered to act representing the full electorate. We did it with
> public actions.
>
> As far as I know, there was no "secret dealing" or "backroom negotiation,"
> but there could have been. Why not? Essentially, *can the people discuss a
> matter privately?" If the people can, their representatives can. The
> electors are responsible to those who gave them their voting power. They
> are known, and their *actions* -- as distinct from what might have been
> said privately -- must be visible. Attempts to implement systems like this
> with computer systems to anonymize the actions are a Very Bad Idea.
> Dangerous.
>
> I have periodically worked on concepts for dealing with small-scale
> coercion. Large-scale coercion, with Asset, I consider not a real hazard.
> There are ways to reassign votes from electors that get less than N votes,
> basically, electors would vote separately when they register to be
> electors, delegating their votes to a ranked list, and that would be
> secret, in a sealed envelope (with their names on the outside). I won't
> give more details. It's useless to design these systems in detail long
> before actual implementation....
>
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