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

[Abd ul-Rahman Lomax]

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....