# [EM] Condorcet strategy spreadsheet (was, ...maybe it should be about Condorcet...)

Jameson Quinn jameson.quinn at gmail.com
Sun Jan 31 11:18:31 PST 2010

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2010/1/31 Juho Laatu <juho.laatu at gmail.com>

> 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.
>

>
> 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. 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, 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.

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.

>
> Juho
>
>
> On Jan 29, 2010, at 6:17 PM, Jameson Quinn wrote:
>
>
>
> 2010/1/28 Juho Laatu <juho.laatu at gmail.com>
>
>>
>> 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.
> 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
> 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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>
>
>
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