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

[Juho Laatu]

Yes. It is not easy to give exact numbers on how often strategies are  
possible in Condorcet. Your calculations give one good estimate on the  
frequency of some of the key vulnerabilities. I tried to list also (in  
my old mail below) additional factors that make the strategies even  
less useful in practice. They may be quite difficult to estimate  
numerically since different societies may have quite different levels  
of willingness to apply strategies, different party structure,  
possibility to control and coordinate the voters, acceptance of  
strategic behaviour etc.

Another approach to resistance against strategies is to study when and  
how the voters should apply some strategy. One may have generic  
strategy recommendations that voters may apply in Condorcet elections.  
Or alternatively specific recommendations for one election when one  
already has some opinion polls available (and when one can pick the  
voter opinions by hand - maybe some realistic set of votes though). I  
haven't seen any good generic recommendations that could be applied in  
typical real life political elections. Even the second challenge of  
election specific recommendations 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?

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. 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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