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We cannot determine a collective opinion, if those concerned do not state their individual opinions, if they vote only ‘no’.   Logically, an ‘Option X, yes-or-no? (‘remain-or-leave?)’ ballotcannot identify “the will of the people”.

Furthermore, when there is no majority for any one thing, there is a majority against every single thing. In June 2016, a majority vote on ‘EU…?’, or ‘Customs Union…?’, or ‘WTO, yes-or-no?’would all have given a majority against.  Brexit was a nonsense.

Thirdly, if and when there are more than two options on the table, an ‘Option X or option Y?’ ballot would also be inadequate.  The outcome could well depend more on the choice of options, and rather less on the opinions of the voters.  Furthermore, as might happen in the House of Commons, a ‘Johnson’s deal or no deal?’ ballot would be open to interpretation: did those concerned vote in favour of ‘X’ or in opposition to ‘Y’?

All in all, majority voting is a blunt instrument which can be inaccurate if not indeed hopelessly wrong.  Consider three persons holding a debate:* Ms i suggests a motion, option A; Mr j moves an amendment, which if adopted would produce option B; Ms k moves a second amendment, for option C; and there’s the status quo ante, option D.

In debate, Ms i has preferences, A-B-C-D; Mr j, B-C-D-A; and Ms k, C-D-A-B. So they first debate and then vote for their preferred amendment, B v C, which B wins, 2:1.  Next comes the question of whether to amend, A v B, and A wins, 2:1. Finally, the substantive or the status quo, A v D, and D wins, again by 67%. Yet all three voters prefer C to D!  So on some occasions, majority voting can be inaccurate if not indeed wrong.

The above is an example of the paradox of voting, for A is more popular than B, which is written A > B; and in fact A > B > C > D > A >… which goes on and on for ever!

So, for a modern pluralist democracy, majority voting is inadequate.  A better methodology would allow the motion to be moved as one option, amendments to be accepted in the form of different options, and for all concerned to cast their preferences on (a short list of) all relevant options.  So, how should such preferences be analysed?

Consider 14 voters, with preferences on four options, A-B-C-D, as shown in table I.*

Table I​​A Voters’ Profile

Option A, with 5 in number 1st preferences but 9 bottom preferences, is obviously very divisive; C a little less so; B has more overall support; option D, however, the 1st or 2nd preference of every voter, would appear to best represent the collective will.  But what happens in practice?

Well, in a plurality vote, it’s A-5, C-4, B-3, D-2, so A wins.  In a two-round ballot, A and C go into the final which, if the voters’ preferences stay the same, C wins, 9 to 5.  With AV (IRV or STV), stage (i) is A-5, C-4, B-3, D-2, so D is out, and its 2 votes go to Bfor a stage (ii) score line of A-5, C-4, B-5, so that’s the end of C, and its 4 votes go (not to D which has been eliminated but) to B, so B wins on 9.  And in a points system – a 1st preference gets 4 points, a 2nd gets 3, a 3rd 2 and a 4th 1 point – the scores are A-29, C-31, B-36, D-44, so D is the winner.

The Citizens’ Assembly recommended multi-option referendums.  This article would go further.  Whether in a parliamentary or a national poll, a contentious issue should be subject to a preferential points vote, not least because, when there are indeed three or more options on the table, the Borda and Condorcet rules “are the two best interpretations of majority rule,” (Oxford Concise Dictionary of Politics, 2003, p 139).  Secondly, for a fringe group of extremists, the DUP, to be in power, while other more popular parties – Labour, Lib-Dem, SNP – are not, is ridiculous; majority rule governance should go superseded by all-party power-sharing.

Finally, on Brexit: any ballot in the House or any second referendum should be multi-optional: to draft an ‘Option X or Y?’ to satisfy all opinions would be impossible; whereas an ‘Option W, X, Y or Z?’ question would be only difficult.

Peter Emerson

Director, the de Borda Institute

www.deborda.org

*​Examples taken from Majority Voting as a Catalyst of Populism (Springer, Heidelberg), launched in Belfast on 26th Sept.

​https://www.springer.com/gp/book/9783030202187