As disenchantment with Tony Blair boosted the Liberal Democrats, Labour has been playing a familiar card for all it’s worth: “Join ranks against the Tory menace!” But should the LibDem supporters pay heed or seal their ears to the sirens of strategic voting?
Here is Blair’s heir apparent, Gordon Brown, pleading in The Guardian:

Thursday’s result hangs in the balance for one main reason: not because of the strength of the Conservative party today, but because of the reluctance of some of our former supporters to vote Labour.

But there is no advance for the progressive cause if a Labour vote switches to Liberal Democrat in a Labour-held seat where the Conservatives are second, and so allows the Conservatives in by the back door.

Needless to say, the background is the UK’s First-Past-the-Post System (FPPS), which gives a marked incentive to vote strategically in order to avoid the notorious spoiler effect. Specifically, it invites a compromising strategy, whereby one votes for an alternative other than one’s true preference because it has better chances. But is that ploy as good as its reputation?

In a superb little article from last year, Empty Moat hits the pig on the snout:

Tactical [=strategic] voting is probably overvalued by millions of would-be rational voters in first-past-the-post elections. These citizens suffer losses in individual representation, and the political systems they participate in will tend to lose the strengths of democracy to the weaknesses of mob psychology.

Approaching the problem from a Rational Choice-theoretical point of view, he defines the net expected utility for a voter as the sum of three factors: the Immediate-Election Utility, the Policy-Shift Utility, and the Future-Election Utility. Let us adopt his terminology while expanding his analysis a bit.

Immediate-Election Utility

Empty Moat defines this as follows:

The expected Immediate-Election Utility is determined by the desirability of the candidates’ policies (or, more accurately, the desirability of the policies that will be successfully enacted by the candidate) weighted by their respective chances of victory in the current election.

From this flows the rationale of the compromising strategy, as articulated by Anthony Downs in a classic treatise:

A rational voter first decides what party he believes will benefit him most; then he tries to estimate whether this party has any chance of winning…. Hence even if he prefers party A, he is “wasting” his vote on A if it has no chance of winning because few other voters prefer it to B or C. The relevant choice in this case is between B and C.

An Economic Theory of Democracy (48). Addison Wesley: Boston 1957.

Now, many people under FPPS do indeed worry that their vote, if not cast for the winner, is a ‘wasted’ one. But consider: How is it any more wasted than the spurious votes for the winner, of which there are typically thousands? Clearly, in terms of Immediate-Election Utility, any vote is wasted that fails to affect the outcome. The common illusion to the contrary is perhaps due to the satisfaction of ‘belonging to the winning team.’ In fact, it could be that many vote for the expected winner partly to associate themselves with the winner – an hypothesis it might be interesting to test.

Undeniably, the Immediate-Election Utility of compromising often exceeds that of voting sincerely. But so what? The Immediate-Election Utility is anyhow negligible, as even in a small constituency the likelihood of any given vote being decisive approaches nil. Indeed, the so-called Paradox of Voting inspired by Downs’ above cited work drives this home: Why does anyone bother voting at all? After all, the expected utility of doing something else with one’s time should dwarf any hope of swaying the election. So if queing up makes sense, it presumably is not because of Immediate-Election Utility. (Some game-theoretical models question this but are indeterminate.)

Why, then, might it be rational to vote from an instrumentally rational perspective? If we broaden the focus to include longer-term utility considerations, the mystery largely dissolves; but so does the case for a compromising voting strategy.

Policy-Shift Utility

One reason to vote is to convey one’s will to the parties to impact their nominations. Empty Moat sums it up impeccably:

The expected Policy-Shift Utility is determined by the effect a vote will have on the policy positions of the various parties, making their respective candidates more or less favorable. A vote is the strongest indicator of voter preference, and the best predictor for behaviour in future elections. Competing parties will tend to shift policies to capture votes. A vote cast for a compromise candidate could have a negative marginal Policy-Shift Utility, since it attracts all parties toward the compromised policies rather than toward the preferred policies.

Furthermore, in cases where the Immediate-Election Utility of a compromise vote is highest (close races), the Policy-Shift Utility of a true-preference vote is also high. Parties in close competetion have more need to capture votes, so a true-preference vote would have more policy-shifting utility.

By supporting the compromise party over their first choice, voters positively encourage it to ignore their concerns while petitioning them, Gordon Brown-style, to always circle the wagons ‘one more time.’ In that sense their votes are worse than wasted.

Future-Election Utility

Then there is party-building. Empty Moat:

The expected Future-Election Utility is determined by the effect a vote will have on future election results. A vote for a party will contribute to an informational cascade of three parts:

  • It will increase recognition of the party (this yields diminishing returns for larger parties, until it becomes negligible), which will help some voters discover the party as their true preference.
  • It will increase the respectability of the party. Voters with limited information on the various policies and related consequences of their choices will draw some information from the expressed preferences of others.
  • It will increase the recognized viability of the party. The expected utility of voting for the party will increase for other voters.

When you cast a compromising vote, all those benefits transfer from the party you prefer to its rival.

We can add a fourth effect: You help perpetuate the very system that under-represents your position. For just as, in accordance with the principle known as Duverger’s Law, FPPS promotes a two-party system, the latter also favors FPPS. In the UK, neither Tories nor Labour has the slightest interest in a more proportional arrangement. Hence a vote for one of them is a vote for the status quo, where a large body of opinion is unrepresented in the halls of power.

Non-utilitarian factors

Besides the longer-term utilitarian considerations we have looked at, there are possible non-utilitarian, though not thereby irrational, reasons for voting. These ascribe intrinsic value to voting and in so doing, strengthen the case for voting sincerely.

For instance, voting might be seen as a civic duty, a natural interpretation of which is to select the best available candidate as one sees it. Voting can also be viewed as a manifestation of fellowship with kindred spirits, or even as a kind of existential choice that helps express and fix one’s identity. But that requires for people to vote their conscience.

So why not vote Nader, then?

An objection may occur to some. It may seem that the argument set forth above, to anyone favoring Nader’s platform over Kerry’s, would justify voting Nader in the recent US election. And reasonably or not, that might be seen as plainly a reductio ad absurdum of said argument. But a reply is at hand: Nader, by running as a likely spoiler against the only realistic challenger to an incumbent so diametrically opposed to his platform, arguably proved himself unfit for public office. Unlike any given vote, his choice might have altered the outcome, and it thus reflects poorly on his judgment, or character, or both – giving everyone a reason to avoid him.

Now, one could make a similar charge against LibDem candidates in constituencies like those described by Brown. Disanalogies abound, however. Unlike voting LibDem, voting Nader would have little Future-Election Utility, since he wasn’t building a party. And while it might have a certain Policy-Shift Utility, a vote for the comparatively less peripheral LibDems would surely have much more. Finally, many progressives would think a Bush reelection far more dangerous than a Tory in 10 Downing Street.

To conclude then: Let us hope the Brits have left strategy to generals and chess players, and voted with their hearts.