On Jan 31, 2010, at 9:18 PM, Jameson Quinn wrote:
.
2010/1/31 Juho Laatu <[email protected]>
Yes. It is not easy to give exact numbers on how often strategies
are possible in Condorcet. ...Even the second challenge of election
specific commendations based on already available information is
hard to meet.
The spreadsheet is about trying to find such strategies.
There have been quite a number of (non-political) Condorcet
elections but I have not seen anyone point out any obvious strategic
opportunities even after the elections. Maybe this also says
something about how common the vulnerabilities are (more experiments
needed though).
So, even when there is a theoretical vulnerability that some set of
voters could use to improve the end result from their point of view
by altering their votes, that may still be quite far from practical
implementation of the strategy. Have you maybe generated some rules
that the voters or parties/candidates could recommend to implement
some of the strategies in real life?
The fundamental thing you need for any strategy to work is a
(potentially) "cyclical" election. That is, you need to know that
(at least aside from your own group of voters) ABC + BCA + CAB > CBA
+ BAC + ACB. Let's take real cycles first, and potential cycles in
the next paragraph. Real cycles very hard to find in real world
elections; if A voters hate C, then C voters tend to hate A
symmetrically. Thus, IMO all the scenarios that the spreadsheet
explores are more-or-less unrealistic; I can't make up good stories
about how they could happen in real life.
In principle "natural" cycles could occur in real life. Let's say
there are three voter groups (33%, 33%, 33%). Each group is mainly
interested in one topic (A, B, C). We have three candidates (C1, C2,
C3). The time and effort that candidate C1 allocates to different
topics is A=>80% B=>20%. C2 allocates B=80% C=20%. C3 allocates C=80%
A=20%. As a result the voters are likely to vote so that candidates
C1, C2 and C3 form a preference cycle. Everything is quite normal
(although simplified, but more complex sets of opinions and candidates
will not spoil this example). The three candidates just happened to
plan their campaigns so that they generate a cycle. That could well
happen.
However, I have found situations which, if they did occur, would
have an obvious strategy for some voter groups. Basically, if you
know there'll be an A>B>C>A cycle, and you can guess A will probably
win the tiebreaker
One of the polls before the election might indicate so.
, then B>C>A (by definition, under 1/3 of voters under most
tiebreakers) should vote C>B>A to elect C, and B>A>C voters (by
definition, a small minority - under 1/6 of voters) should vote
B>C>A to help elect B. Note that these strategies contradict each
other - but either one is somewhat robustly rational on its own.
I believe we are by default talking about large public elections. Now
we have the problem of informing the voters on what to do. Candidate
B's campaign office can not propose B>C>A voters to vote C>B>A in
order to elect C since B>A>C voters would not like that. Such
recommendations might also sound like B will give up. It is maybe
better (and more typical) for B to continue campaigning, claim to a
potential winner and try to get the missing votes somewhere (so that B
would win already with sincere votes). Candidate C's campaign office
might recommend B>C>A voters to vote C>B>A, but candidate B and
candidate B supporters might think this is just a campaign trick. C
office might give this kind of recommendations (propaganda) even if
they would not believe that the poll is accurate and that voter
behaviour will be similar at the election day.
I just picked some points above to show that it is not easy to control
and achieve the intended results in this kind of strategy campaigns.
Do we have some nice set of poll answers that some campaign office or
voters themselves (one by one, maybe getting assistance from the media
on how strategic voting works in Condorcet) could study and use as a
basis for strategic voting recommendations, and then implement this
strategy successfully? (= working election specific strategy) Can the
campaign offices trust on some particular poll enough to make their
move based on that? Public strategic recommendations may also cause
reactions among the voters (sincere changes of opinions and other
strategic moves). (And how abut continuing positive campaigning to
change the opinions of the voters before the election day?)
But all of that assumes a knowable honest cycle - implausible to me
for the reasons of symmetry given above. The more plausible
situation is if there's a potential to strategically create a cycle,
but no real cycle. For instance, say the election is a one-
dimensional, partisan ABC battle, with B in the middle; you are a C
voter; you know that C is not the likely winner; you have reason to
believe that there are more BCA than BAC votes; and you're willing
to dishonestly vote CAB and risk A beating B (that is, you don't
really care about the difference between A and B). This is still
just a bit implausible - if C voters think that B is closer to A
than C, why do B voters think that C is closer to them than A?
Moreover, most Condorcet tiebreakers would tend to give this
election to B or A, even in the face of strategy, unless the fake-
CAB strategists were surprisingly unified. If the strategy does
"succeed" in picking C, that means that C would have won a plurality
election. So this is the "best case" real-life strategy, and it's
pretty weak - unlikely to succeed and likely to backfire - and the
result is no more "pathological" than what we're already used to. I
can imagine it happening rarely, I can imagine being very frustrated
by it if I were on the wrong side - but honestly, I can't say that
the C voters wouldn't deserve the victory. That is, if this strategy
is rational, it is likely that C is the true Range winner, though
not the honest Condorcet winner.
Yes. You already identified a number of problems that the C supporters
will face, so I don't need to try to find more.
In order to prove that Condorcet is not safe enough in typical
elections it would be enough to present one concrete and rational
example (= working election specific strategy) that the campaign
offices could recommend and voters could then implement, or that the
voters could independently apply. Any of the discussed categories
would do. But it seems that such examples are not very easy to find.
Anyone, any good examples in your mind?
Juho
Juho
On Jan 29, 2010, at 6:17 PM, Jameson Quinn wrote:
2010/1/28 Juho Laatu <[email protected]>
To be exact, one could also break an already existing cycle for
strategic reasons (compromise to elect a better winner). And yes,
the strategies are in most cases difficult to master (due to risk
of backfiring, no 100% control of the voters, no 100% accurate
information of the opinions, changing opinions, other strategic
voters, counterstrategies, losing second preferences of the targets
of the strategy).
Yes. Some months ago, when I proposed "Score DSV" voting, I did
some playing with a spreadsheet to see the true individual benefit
and social cost of various types of strategy in various 3-way
condorcet tie scenarios. A link to the spreadsheet is here. There's
a lot more black magic there than I care to explain fully - that's
why I didn't share this earlier - but I think that something like
this is useful in exploring the nature of strategies. So, I'm
putting it out there for any geeks like me who are interested.
Here's a "quick" (that is, incomplete) explanation of how it works.
If you want to skip the technical details, there's a couple
paragraphs about what I learned from it at the end of this message.
...
The voting system used, in all cases, is Score DSV. This is a
system which uses Range ballots and meets the Condorcet criterion.
As a Condorcet tiebreaker, it is intended to give the win to the
candidate whose opposing voters would be, overall, least motivated
to use strategy to defeat her. (Of course, this "least" is after
the normalization step. This is inevitable since normalization is
the only mathematical means of comparing preference strength across
voters.) Still, while the mechanics of Score DSV are unusual for a
Condorcet system, its results are not so much. A typical Condorcet
system would give results which are broadly comparable. (Actually,
since only the 3 candidate, no-honest-equalities case is
considered, the winner and all non-equal-ranking-based strategies
are mutually identical for a large set of Condorcet systems,
including, IIANM, Schultz, Tideman, Least Margin, and others, but
not Score DSV).
The spreadsheet works by first creating a 3-way Condorcet tie
scenario. To do so, you set 7 parameters, the red numbers in the
blue area. Feel free to change the red numbers, but please, if you
want to change the spreadsheet in another way, use a copy. The
basic parameters are:
-In the column "num voters", the size of the three pro-cyclical
voting groups - ABC, BCA, and CAB. Without loss of generality, the
first group is the largest.
-To the right of each voter number is the average vote within that
group. All groups vote 1 for their favorite of the three candidates
and 0 for their least favorite, but you can change their honest
utility for the middle candidate to any number between 0 and 1.
-The voter population is assumed to have some anticyclical voters
(ACB, CBA, and BAC). However, you do not set these numbers
directly. The anticyclical voters are assumed to be a "bleed over"
of the cyclical voters. For instance, if the ABC voters assign a
relatively high utility to B, then some fraction of them will
actually become BAC voters. To change the overall size of the
anticyclical vote, change the value in cell B1 ("cohesion power").
A higher value there will give a smaller anticyclical vote. Values
should be 1 or greater. Lower values are probably more "realistic"
but lead to weaker (or even broken) condorcet cycles. Values over
3-4 lead to essentially negligible anticyclical voters.
Once your scenario is created, the spreadsheet will calculate the
utility of various strategy options for the different voter groups.
Each strategy is placed to the right of the group to which it
applies, and continues through the row. Each strategy has intrinsic
values and calculated values. The intrinsic values include the
strategy name, the candidate it is "for" (intended to favor), the
candidate it is "against" (intended to disfavor), and the strategy
(if any) it is intended to respond to or defend against.
The values calculated for each strategy include:
-Works: this is true (green) if the strategy has any hope of
working, and false (red) if not. If this value is false, the rest
of the row for this strategy consists of GARBAGE values, and should
not be considered.
-Undefensible: true if there is no rational strategy which could
defend against or change the results of this strategy.
-Payoff/voter: if the strategy works, how much "utility per vot"
would be gained for this voter group?
-Semi-dishonesty/risk: by how much would the voters in question
have to change their ballots in order for this strategy to work?
Or, equivalently: if the strategy ends up backfiring for some
reason, how much utility would this voter group lose? It is
reasonable to assume that the higher this number is, the more
difficult it will be to organize this strategy. This is expressed
as a total, not a per-voter number, since a strategy which requires
the cooperation of a lot of voters will be harder, just as a
strategy which requires voters to "hold their nose" more strongly
and vote a seriously dishonest ballot (rather than just a minor
change from their true utilities).
There are also "probabilistic" values calculated for each strategy.
The probabilities are run using the assumption that there will be
some random noise in the results. The quantity of this noise is set
by the "effective uncorrelated electorate size" (EUES, cell Z24). A
lower number here means that the noise will be more significant. If
the EUES is 30, then the actual "election day turnout" will be a
poisson distribution around 30, and each voting bloc will turnout
in a poisson distribution of the appropriate fraction of 30. This
"noise" could simulate polling error (that is, voter uncertainty of
the true makeup of the electorate due to statistical weakness of
polls), voting-day error (that is, turnout fluctuations due to
random chance events), or true error (last-minute swings in the
electorate, polling bias, etc.)
Thus, each voting bloc has an "expected value" for the election,
and each strategy has an expected payoff. This payoff can be
negative because it includes the probability that the strategy will
backfire. In order to calculate these expected payoffs, there are
two more parameters for "strategic cohesion" of offensive and
defensive strategies (cells Z27, Z28); this is the portion of the
group in question which may be expected to use the strategy (since
there will always be some fraction of nonstrategic holdovers).
....
The spreadsheet overall is quite slow in Google Docs. If you want
to play with it more than a small amount, it's probably worth
downloading a copy and opening it in your favorite desktop
spreadsheet application (ie OpenOffice, Excel, etc.)
What I learned from this spreadsheet is that, in a Condorcet tie
situation, there are always some strategies which are rational. As
far as I can tell, while it is possible for a good system to
minimize the strategic incentives, it is not possible to create a
system without at least some scenarios where the expected payoff of
a strategy is significant. This holds even in the face of a fair
amount of "noise", and even with a system designed to minimize
strategic payoff. Before making this spreadsheet, I had hoped that
Score DSV would be good enough that, with some noise, the risk of
any strategy would be enough to discourage its use, but that is not
the case.
Still, to find scenarios where a strategy clearly pays off takes
some work. I have not done any systematic statistical sampling, but
I'd say that with Score DSV, such scenarios represent around 1/3 of
condorcet ties. Given that condorcet ties should probably occur in
somewhere between 1% and 15% of real-world elections, and that the
group of voters for whom strategy is rational is typically around
25% of the electorate, that means the average voter will have a
rational strategy less than 2% of the time (perhaps far less). I'd
say that that's negligible enough to hope that some kind(s) of
honest normalized voting would be a dominant strategy. Certainly,
it seems to me that this shows that it's unwarranted to imagine
100% strategy in Condorcet, or to compare the results of Bayesian
Regret simulations from N% strategy in Condorcet systems against
the same N% strategic voters in Range systems.
Jameson Quinn
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