At 12:35 PM 6/22/2008, Terry Bouricius wrote:
Ms. Dopp has requested a clearer example of how Range and Approval voting
can experience a spoiler scenario (through violation of the Independence
of Irrelevant Alternatives (IIA) Criterion). Although her inability to
follow Chris's logic led her to use extremely disrespectful language, I
will assume she was having a bad day and was just extremely frustrated.
Perhaps. Or perhaps she was the newcomer saying that the emperor has
no clothes, which can be extraordinarily rude, if you think about it.
Here is a simple example, that I hope she can follow...
Certainly I'll look at it closely!
How a voter scores a particular candidate (or whether the candidate is on
the positive or negative side of an approval cut-off) depends on what
other candidates the voter has to compare the candidate to.
The word "score" as being used by Bouricius implies relative scoring,
most notably what in Range would be called "normalization." These are
*not* absolute ratings, and aren't commensurable from one voter to
another between various election configurations.
If the voter thinks candidate A is okay, and B is horrible in a two way
race, the voter will likely score A as a 10 and B as a 0 (approve A and
not approve B). [Rather than insert an Approval Voting translation for
each point from here on I will just use a Range example, though the
dynamic is the same.]
Yes. That's correct. But the same, of course, is true if B is merely
less than okay. Bouricius is teetering, here, on confusing Range with
Approval. Voter's don't "score" candidates in Approval except as A
and B, and we may assume some underlying rating, which will be,
properly, continuous, not set up in discreet steps from 0 to 10. And,
because this is a single voter, normalization has no effect. The only
thing that has an effect is where the voter sets the approval cutoff,
which is a decision made -- quite properly -- based on the election
environment. In recent posts to the Range Voting list, Smith has
shown how serial Approval elections cause voters to lower their
approval cutoff, perhaps, as new candidates are also introduced as compromises.
If there are 100 voters and 55 prefer A>B and 45 B>A, this two-way race
could end with a total score of 550 for A (55 voters giving a 10 and 45
giving a 0) to 450 for B. Thus A is both the de facto majority choice as
well as the Range score winner.
Using "score," multiplied by 10, for Approval results looks to me
like Bouricius is setting something up.
Now comes the spoiler...What if candidate C decides to run as well? It
happens that a significant portion (let's say 25 out of the 55) of the
former A supporters who care most about issue X view candidate C as a
fantastically superior candidate to A or B (though they still prefer A
over B as well). It seems likely that many of these voters would feel the
need to reduce the score of ten they otherwise would give to A to make
room on the scale so they can indicate how superior C is to A. These 25
voters might now score the candidates as follows, A=5, B=0, and C=10. In
other words, the score that A now receives from some voters depends on
whether C has entered the race. The B supporters who generally don't care
much about issue X view C as just another version of A, so give this new
candidate a 0 as well. Under this entirely plausible scenario, with C in
the race, now the total scores might be A now only gets 425 (30 x 10 and
25 x 5), while B still gets 450 (45 x 10) and C gets 250 (25 x 10).
This is such a complex explanation that, at first sight, I'm tempted
to totally ignore it. Sigh.
A new candidate, C, is considered "fantastic" by 25/55 of the A
supporters. So they switch their votes. As would be expected, surely,
from such an introduction, results can change. But Bouricius has
made, actually, quite a preposterous assumption. He's assuming black
and white ratings for all other voters. Nearly half the A supporters
think C is so much better than A that they think he's better than A
by as much as A is than B, yet, *none* of the other voters are moved
by this candidate? So it is *not* an "entirely plausible scenario."
The real matter is much simpler.
First of all, technical compliance with election criteria can be
highly misleading. As an example, Approval is commonly asserted to
fail the Majority Criterion, and supposedly this is a bad thing.
After all, majority rule and all that. However, Approval only fails
the special definitions of the Majority Criterion invented to deal
with the problem of applying it to methods which allow equal ranking
at the top. And so whether it fails or not depends on the precise
definition, it's no longer "objective." Secondly, even granting these
definitions, what are the conditions under which it fails? It fails
when more than one candidate is approved by a majority. How common is
this? Not terribly! It practically never would happen in a two-party
environment. It could happen with a third candidate, when it would
likely be quite a good outcome. Range makes the matter clearer, and
Range and Approval with runoff requirements when majority preference
isn't clear would do even better.
Bouricius glossed over the most important fact: did the C voters
approve of B or not? That's a decision that they would make in the
real election environment, and not one that can be assumed from the
ratings. Given the election environment, and standard Approval
strategy, it's *very* likely that they would also Approve A, not just
C, and so A continues to be the winner.
Now, by making the election arbitrarily close, and assuming C voters
who radically revise their preference for A (not the example given),
we can show a shift.
Thus C has "spoiled" the race for A. The entry of C caused B to go from a
loser to a winner.
This is not, however the classic spoiler effect. There is a
contradictory assumption in the example: that voters withdraw their
approval of A because of the entry of C, while, at the same time, B
remains a very strong contender (and, with C in the race, the
frontrunner in first preference). This is a very bad time to vote
Approval as if it were Plurality, which is what Bouricius has the voters doing.
The most bizarre aspect of the example is that C is considered truly
great by almost half of the A voters, and nobody else is moved at all
by C. Voter opinions exist on a continuum. Classical ranked voting
analysis completely disregarded this, and it's still very tempting to
analyze Approval and Range Voting using highly simplified -- and
therefore possibly deceptive -- analysis. The only approach which
truly deals with the problem is simulation, which can assign voters
votes based on various assumptions about utility distributions.
The identical dynamic can be demonstrated for Approval Voting using voter
decisions about where to draw their approval cut-off line, once C enters
the race.
That's correct, and if you have a quarter of the voters making
basically stupid decisions, they can end up with a bad result. Those
voters preferred A to B, strongly by the assumptions in the example.
For them to not approve A doesn't make sense. So they would approve A!
As I've often stated when dealing with this problem, what happens if
the Messiah is suddenly placed on the ballot? With Approval, it is
*possible* for voters to approve the Messiah and also another
candidate, even though they vastly approve the Messiah to the other
candidate. ("The Messiah" is my code word for the absolute best
candidate possible among the entire universe of candidates.) Whether
or not voters will do this or not depends on how they see the
election possibilities: is the Messiah a realistic candidate. And if
write-ins are possible, indeed, we could say that every possible
candidate is on the ballot. But how many actually vote for the
Messiah, in Plurality, and how many would do so in Approval? Voters
will only bother with choices that actually are realistic, and with
25% first-rank support, C doesn't have a chance, probably. Now, in a
real election in real politics, those C voters would know that
additional approvals, were the situation actually as described by
Bouricius, weren't appearing. So they would vote for A as a backup
vote, which then allows their otherwise-favorite, A, to continue to win.
In real-life, as well, a 2-party system isn't going to change into a
3-candidate situation overnight. Voters, by the time a scenario
appears such as Bouricius describes (actually, not that scenario,
which is preposterous, but a more reasonable one), voters would
understand the risks of bullet voting, which is the only action that
is dangerous here.
Bouricius, by blending Approval and Range in his analysis, obscured
the issues. He counted the "ratings" as if they were votes, when, in
fact, if the election were Approval, those intermediate ratings
wouldn't be votes, and left silent was the strategy by which voters
convert their "ratings" to votes.
Again, Bouricius is using normalized utilities, not absolute ones,
that is clear from his shift of the rating for A from 10 to 5 by the
entry of C, for the C supporters.
What would happen in reality? Standard Approval strategy: pick the
frontrunners, vote for your preferred one, vote for one and not the
other. Who are the frontrunners? A and B. C isn't a frontrunner. C
would then be, by standard strategy, for 25% of the voters, an
additional approval. Not a spoiler.
Same strategy in Range: pick the frontrunners, vote 0 for one and
100% for the other. Then add other ratings relative to those. That
would indicate, in this situation, that 25% of voters would vote 100%
for C, everyone else zero. That's not a frontrunner at all. That's
the third place candidate. Now, voters like to express preferences,
so the C voters would derate A, considering the strategic situation,
not to 50%, but to 99%, probably, just enough to indicate the
preference. Some would go lower than that, but, rememember, the votes
for other candidates would be similarly complex. The other A voters
are highly unlikely to sincerely rate C at zero, and those votes
would raise the total votes for C. Likewise, the B voters would be
unlikely to consider A and C as being identical.
The fact is that simulations show that, with a variety of assumptions
about voter strategy, Range is optimal; there is now work showing
that, indeed, it's *uniquely* optimal, but that's a debate for
another way. Approval is a Range method, simply the most blunt one,
and voter averaging -- something entirely neglected by primitive
analyses such as those of Benham and Bouricius -- makes Approval more
accurate than otherwise may seem the case. (A binary detector can
detect intermediate values if the threshhold of detection is swept
across the analog range, which is what happens with voter
populations, we expect. Each vote is black and white, but the average
voters reveal the underlying preferences, at least to some degree.
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