[EM] another concern - the opposite of the Spoiler Effect - *Packing*

[Abd ul-Rahman Lomax]

At 08:30 PM 6/27/2013, Benjamin Grant wrote:
>Something else came up while I was analyzing 
>some voting methods.  If you have a 
>disproportionate number of political leaning in 
>an election, some voting systems go awry.

I didn't know what this meant when I first read 
it, and there is a grammatical error contributing 
to that. Benjamin, would you mind proof-reading 
your posts? Yes, some people can't do that, and 
if you can't, okay, but ... just understand that 
you lessen the number of people who will read 
what you write if the lead paragraph is incomprehensible.

Then I guessed what it mean. And that guess was 
wrong. In fact, reading the further explanation, 
the introduction just doesn't make sense. It means something else.

>
>There may be a criterion for this, this is what I mean.

Condorcet criterion, for starters. The nameless 
Range Criterion (i.e, maximized expressed social 
utility.) Some voting systems don't collect enough data to handle this.

>Let’s say that you have three total 
>candidates.  one is conservative, two are 
>liberal, none are moderate.  If the majority of 
>the electorate is conservative, then it may make 
>sense that a conservative gets chosen.  However, 
>in some systems – say one in which each voter 
>gets one positive vote and one negative vote to 
>cast – having more candidates of a particular 
>“wing” can hurt you. Continuing this example, if 
>we run Gore/Nader/Bush, both Gore and Nader 
>supporters give their negative votes to Bush, 
>casting their positive votes for their own candidate.

Standard vote-splitting problem.

>
>If Gore supporters are 36%, and they vote Gore 
>+1, Nader 0, Bush -1; and Nader supporters are 
>10%, and they vote Gore:0, Nader +1, Bush -1; 
>and Bush supporters are the remaining 54% and 
>they vote Gore -1, Nader 0, Bush +1

>
>Nader wins. Even though 54% of the people voted 
>for Bush. Even though only 10% voted for Nader.

The stated votes are *insane.* Not that this 
matters, people propose insane voting patterns 
all the time, to make this or that point. It 
would help to recognize it. ("I am making up this 
insane voting pattern just to show how the system would handle it.")

That is, the stated problem is "too many voters 
in one wing." But the voting patterns establish 
Nader as in the center. You simply *said* that 
Nader was "in the same wing," but then you did 
not have the voters vote that way.

Of course, you can define a "Wing" any way you 
like, by placing the "center" where you choose.

Voting that way, as in the example, we have this situation:

36% of the voters, Gore supporters: Nader is 
closer to them than Bush. Consisent with Nader 
being Center, not completely consistent with 
Nader being Left. (for some Gore supporters, 
Nader, if to the left, would be futher from them 
than Bush. But if there is a wide enough gap 
between the Gore and Nader factions, it could 
happen that all Gore voters would vote this way. But they are in a minority.)

10% of voters, Nader supporters: Gore is closer 
to them than Bush. Consistent with Nader being 
Left, not consistent with Nader being Center. 
Center factions will split on who is closer, Left or Right.

54% of voters: Nader is closer to them than Gore. 
Not consistent with Nader being Left, consistent with Nader being Center.

 From the voting pattern, it's conclusive: Nader 
is in the center, as viewed by the majority, and 
consistently with the rest of the votes, in spite 
of the stated claim that there is no center candidate.

There is a problem with +/- range voting, having 
to do with the 0 default that is often assumed. 
But we can look at this election as Range 2, by 
adding a value of 1 to all votes, and considering 
that there were no abstentions. We have a 
situation where *every voter* rates Nader as 
midrange -- election expectation -- or better. 
Nader will win this election in Range, and this 
is an example where Condorcet compliance would 
damage social utility. I have suggested that it 
is defective to accept this result without the 
explicit consent of a majority, and, in this 
case, if a midrange rating is openly an approval 
rating, *every voter has consented.*

The example does not show any problem except in 
the analysis as being a "wing" problem. It *looks 
like* a Majority Criterion failure, except that, 
by giving a half-vote to Nader, the majority 
waived its majority rights, that was not the 
"exclusive preference" that the majority 
criterion requires. The majority approved both 
Bush *and* Nader. And *everyone* approved Nader. 
So why would one think Bush should win?

There is an answer to that, and it would be a 
belief in the Condorcet Criterion as what I used 
to call it, the Queen of Voting Systems Criteria.

>Is this a thing? Kind of the opposite of the 
>spoiler effect – that having many like-minded 
>candidates actually increases the chance that 
>one of them might win, even if their opposition is more numerous?

The example does not show anything about 
"like-minded candidates." Rather, it shows how we 
casn make up things, express them, and it all 
looks sensible to us, because we see only a small 
percentage of what is actually in front of our 
eyes, as we became socialized and "experienced." 
There is a way out of this trap, but few are 
interested in it. It can threaten our *identity.*

Most of us would rather be right than happy.

>Does this only happen with negative votes?  Or 
>can it happen with other methods?

The example shows no effect from negative votes. 
That was noise that helped you to remain 
confused, Benjamin. The exact same "issue" would 
appear with Range 2, i.e,. votes of 2,1,0, and it 
could appear with any Range system. It's a *feature*, not a bug.

The violation is of the Condorcet criterion, 
because Bush wins all the pairwise elections. 
That's because the Criterion pays no attention to 
preference strength. A situation like that 
described shows the breakdown of the Criterion, 
it can occur where a majority has weak 
preferences whereas a minority has strong 
preferences. If that is *actually the case,* not 
just some artifact of defective strategy, then 
social utility is optimized by the violation of 
the Criterion in favor of the range winner.

The essential error here was to treat a Range 
(Score) election as if it were a ranked election, 
because every voter *strictly ranks* the 
candidates, using the three available ratings. 
That won't happen. If the real situation is that 
the left-right axis is occupied by, Left to 
Right, Nader, Gore, Bush, then, if voters vote 
based on axis position, no Bush voters (the 
majority in this model! -- not in real life in 
2000) will min-rate Nader, since they would 
prefer Gore to Nader; and if, for strategic 
reasons (sane if Bush and Gore are frontrunners), 
they min-rate Gore, they would *also min-rate* 
Nader. Otherwise they would min-rate Nader and 
mid-rate Gore. Not mid-rate Nader, ever.

But voters don't vote exclusively based on a 
single axis, that is another general problem with many analyses.