By Leon P. Smith & Warren D. Smith (no relation)
Prior to the 5 May 2011 British referendum on whether to switch to Instant Runoff Voting (IRV; which the British call "the alternative vote") – in which the voters decided by a huge 68-to-32 margin to stay with the plain plurality ("first past the post") system – the BBC published the following study:
If IRV had been used in previous general elections would it have changed the result? This graphic illustrates how the results of the last six general elections might have looked had the 'alternative vote' system been in place. The overall outcome of the contests would not have changed, but the Liberal Democrats would have gained the most seats and the scale of the Conservative defeat in 1997 would have been much greater, the research suggests.
Notes by BBC: The Lib-Dems were formed in 1988 after contesting the 1983 and 1987 elections as the "SDP-Alliance." [Note: This projection assumes that voters still select the same first choice candidate as they did in the first-past-the-post system.]
You can also see the BBC study's underlying poll data (pdf) & some remarks on how they got it.
Further remarks by us. Leon Smith finds that in 1983, 1987, and 1992 the Conservatives were Condorcet "beats all" winners (preferred by a voter majority versus each rival party one on one); while in 1997, 2001, and perhaps 2005, it was Labour. But because the uncertainties in 2005 are fairly large, he concludes that perhaps the LibDems (conceivably even the Conservatives?!) were the Condorcet winner in 2005. Note: the years have different amounts of uncertainty caused by missing pair-preference data, with 2005 having the most. 2001 also has a lot. Hence not all of Leon's conclusions are 100% certain; some have lower amounts of certainty. Leon Smith also finds the LibDems were "the most probable Condorcet second place finisher" every year, meaning that each year, it appears probable that the LibDems were preferred by a voter-majority versus each rival except for the winner. Again, however, that conclusion is most attackable in 2005.
Spreadsheet with Leon's calculations
This all is assuming the pollees honestly told the BBC pollsters their true preference orderings, as opposed to strategically dishonestly altered preference orderings.
The official election results (using plain plurality voting) are summarized in the table below:
| Year | Results (Seat Counts) | Results (Popular Vote %) |
|---|---|---|
| 2005 | Labour=355, Conservative=198, LibDem=62 | Lab=35.2%, Con=32.4%, LD=22.0% |
| 2001 | Labour=413, Conservative=166, LibDem=52 | Lab=40.7%, Con=31.7%, LD=18.3% |
| 1997 | Labour=418, Conservative=165, LibDem=46 | Lab=43.2%, Con=30.7%, LD=16.8% |
| 1992 | Conservative=336, Labour=271, LibDem=20 | Con=41.9%, Lab=34.4%, LD=17.8% |
| 1987 | Conservative=397, Labour=229, SDP/LibDem=22 | Con=42.2%, Lab=30.8%, LD=22.6% |
| 1983 | Conservative=397, Labour=209, SDP/LibDem=23 | Con=42.4%, Lab=27.6%, LD=25.4% |
So each year except perhaps 2005 it appears that there was an unambiguous Condorcet order in which the LibDems placed second (albeit in 2005 perhaps they placed first), but both the official plurality voting system and the IRV system always caused the LibDems to finish way in third place! This suggests that the IRV system would have severely distorted British democracy, while the plurality system they actually used produced an even stronger distortion.
However, that conclusion is based simply on preference orderings stated by pollees, not on the (perhaps varying) strengths of their preferences. To explain what we mean by that, consider the following two fake datasets with 5 voters (each voter expresses her opinion of each party on a numerical scale from 0=worst to 9=best):
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In both the pink and green tables, the preference orders are exactly the same. However, the strengths of those preferences differ considerably. It is clear that in the pink scenario at left, the "correct" winner ought to be the Conservatives. However, in the green scenario at right – with the exact same preference orderings – it is clear that the "correct" winner ought to be the LibDems. This kind of strength of preference data is simply ignored (indeed the voters are never even asked for it) with IRV and Cordorcet. But as you can see, it might make a huge difference to what is best for Britain. Range voting, aka score voting, is a simple voting system which does ask voters for strength of preference information, and which does take it into account.