Condorcet.orgStrategic voting occurs when a voter does not vote his or her true preference, in the hopes that a false one will get a better result. All the methods that people suggest adopting (including plurality) have some element of strategy. Ranked Pairs is no exception.
The most common example of strategic voting is the one from plurality. A voter may vote not for their first choice, but for a later choice they believe is more likely to win. This is called the compromising strategy. For example, if the true rankings of the voters are:
45 ABC
12 BAC
13 BCA
35 CBA
Then, if the voters all vote for their first choice, the result is:
A 45
B 25
C 35
A wins. However, if the BCA voters all voted for C, then C would win:
A 45
B 12
C 47
Of course, the BAC voters could cause A to win by voting A.
A 57
B 47
Ranked Pairs has strategy problems as well, but they may be somewhat unfamiliar to someone who is used to the strategy problems of plurality.
Here is an example of what may be called the burying strategy, that of lowering a candidate in your ranking in the hope of causing a candidate you like better to win:
45 ABC
18 BAC
17 BCA
20 CBA
B is the Condorcet winner, so B will win.
However, if the A-1st voters had instead voted as follows, lowering B in their rankings
45 ACB
18 BAC
17 BCA
20 CBA
Lock C>B 30
Lock A>C 26
Skip B>A 10
Result A>C>B, A wins
However, there are reasons to believe that A will not be able to accomplish this. For one thing, it will be difficult for the A-1st voters to organize such a strategy without letting any of the other voters know, at least in a large scale election. It would be easier to organize in a setting such as a parliament, but then the B-1st voters could judge the likelihood of strategy from A on the basis of past votes.
As well, it is rather risky. For example, if the B-1st voters had ranked C ahead of A, you get:
45 ACB
35 BCA
20 CBA
Now Cis the Condorcet winner. So, a strategy like this can easily back-fire. Voters won't know this precisely how others are voting. If the A-1st voters rank B insincerely last, they could very easily elect C instead of causing Ato be elected.
There is good reason to believe that an electorate that will use a great deal of strategy will have trouble getting accurate polls on which to base the use of strategy. The reason, is that it becomes in the best interest of voters to lie to pollsters (or at least not answer questions). In the above example, A voters were willing to use strategy because C was low in support. If A were to use the same strategy with slightly less support (and slightly more for C) the result could be like this:
40 ACB
18 BAC
17 BCA
25 CBA
Lock C>B 30
Lock B>A 20
Skip A>C 16
Result C>B>A, C wins
So, if a small number of C-1st voters claim instead to be A-1st voters, strategic A 1-st voters will be prompted to increase their ranking of C. This could cause C to be elected.
Finally, if the C-1st voters catch on to the strategy, they can defend against it by ranking B in first place. This gives B a majority of 1-st place votes. Voters may then find it is simpler if everyone just votes their true preference.
Ranked Pairs is also affected by the compromise strategy mentioned for plurality, albeit to a lesser extent. Here, a voter raises a candidate in their rankings in the hopes of electing that candidate, and avoiding the election of a worse one.
45 ABC
35 BCA
25 CAB
In this example, A would normally win. However, the BCA voters could improve the outcome (from their perspective) by voting CBA, which would result in C winning with a majority of first place votes.
This above example will be handled the same by plurality and IRV. That is, they both would elect A, but this can be prevented by a compromise from the BCA voters.
This brings us to an important fact. If you recall, I defined the Condorcet winner in The Introduction. It can be mathematically proven that if a method is majoritarian, that is it always elect a candidate who gets a majority of first place rankings, then the compromise strategy will work in all examples, and only those examples, where a Condorcet winner is not elected. Since Ranked Pairs always elects the Condorcet winner, if one exists, the only examples where the compromise strategy works are those where there is no Condorcet winner, like in the example above.
Since plurality and IRV often do not elect the Condorcet winner, even when one exists, they are much more affected by the compromise strategy. Consider the following example:
45 ABC
13 BCA
12 BAC
35 CBA
Both plurality and IRV elect A as the winner. The Condorcet winner is B. As a result it is possible to use the compromise strategy to elect B. That is, the CBA voters could vote BCA. This would elect B (an improvement from their point of view). Unlike for the burying strategy, there is no counter-strategy that can be used when the compromise strategy is used to elect a Condorcet winner. Of course, I would argue that when strategy is used to elect a Condorcet winner, that the result has actually been improved.
Why do we care about strategic voting? That's an important question. I suggest that there are three main reasons. The first, and I believe most important, is that strategic voting can make the method give worse results. That is, I have given many reasons why I think that Ranked Pairs chooses the best guess for best candidate, if voters vote sincerely. If they don't, the result won't be as good. From this point of view, the goal of preventing strategy is inextricably linked to the goal of picking the best candidate. A method that doesn't choose well, even without strategy, should not be chosen simply because it manages to defend these bad results against strategic voting. From this point of view a method should be judged on the basis of good results without strategy combined with defense against strategic voting.
This is the problem I have with IRV and plurality.
45 A B C
25 B A C
35 C B A
It is possible in this example for the A-1st voters to elect A by the strategy of voting ACB. If you believe that B is the correct winner, this is a problem. However, with IRV or plurality, A will win in this example even with no strategy.
Another way of looking at strategy is to say that strategic voting is inherently bad because it is unfair to non-strategizing voters. From this perspective, the actual results of the election are irrelevant, except in whether strategy is useful or not. From this point of view, the compromise strategy that is so prominent in plurality and IRV is a big problem. In the above example, C voters could improve the election results (from their perspective) by voting BCA. The A voters would have no way of defending against this tactic. Of course, it could be argued that they have also improved the result of the election by electing the Condorcet winner, but from the perspective of avoiding strategy, that is irrelevant.
A third concern is that strategic voting can be used to over-turn the results of a previous vote. For example, after a legislature makes a decision, legislators may try to get the decision reversed by using strategy. And if they have a record of how everyone voted, this can be much easier. This is a particular problem for plurality and IRV, and I suspect one of the reasons that these methods are rarely used by legislatures.
45 A B C
25 B A C
35 C B A
In the above example, the plurality and IRV winner is A. However, the Condorcet winner is B. The fact that they are different guarantees that some effective strategy can be used. If the the C B A voters get the issue before the legislature again, they can switch their vote to B C A, improve the result from their point of view, and there is nothing the A-1st voters can do to defend against this.
This can be contrasted against the use of the burying strategy in Ranked Pairs. If one group tries to use strategy to defeat the Condorcet winner, the counter-strategies mentioned above can be used to prevent it.
So, my point is that selecting the CW (Condorcet winner) is closely related to the issue of strategy. Strategy is highly effective in causing the the CW to win, or to defend it against other strategies. So, it makes sense from a strategic point of view to elect the CW when one exists.