Scottish Affairs CommitteeWritten evidence submitted by Iain McLean, Professor of Politics, Oxford University

A 3—Option Referendum

1. There is considerable interest in a referendum (or referendum question) inviting Scottish voters to vote for or against something currently labelled as “devolution-max”. Those promoting such a question wish it to be put in addition to the referendum question on Scottish independence, the terms of which are currently being negotiated by the Scottish and UK governments.

2. One motive for such a demand is that “devolution-max”, although currently undefined, appears to have majority support in Scotland. The most reputable opinion poll series, Scottish Social Attitudes, has shown that for two decades the largest single group of respondents have opposed Scottish independence, but have favoured more powers for the Scottish Parliament. There are as yet no reliable figures to say whether or not opinion has moved since the recent announcement by the Scottish Government of its plan for an independence referendum, and the UK Government’s response.

3. The academic discipline known as “social choice”, that is, the mathematical study of the properties of choice and election systems, has existed for over 200 years and has a lot to say on the practicality of a 3-option referendum; but it has not featured in policy discussions to date.

4. The most relevant result is that if opinion is single-peaked, then any well-behaved choice system will select the majority-winning option. I define these terms below.

5. Opinion is single-peaked if the options can be arranged in some order such that nobody ranks the middle option(s) lowest. Opinion on constitutional options for Scotland would this be single-peaked if, for instance, everybody whose first preference was Scottish independence ranked devolution-max above no change, and everybody whose first preference was no change ranked devolution-max above Scottish independence.

6. A majority-winning option is an option which wins a majority in straight comparisons with each (all) of the other options on offer.

7. A well-behaved choice system is one which always selects the majority-winning option when one exists. There are rare circumstances, known as a “cycle”, in which no majority-winning option exists (ie, A beats B, which beats C, which beats A). Although of great theoretical interest, this possibility is probably not relevant to the Committee’s current inquiry. However, it must be considered by Parliamentary draftsmen (see below).

8. These criteria rule out an option which has been canvassed: namely using the Alternative Vote (AV), as proposed unsuccessfully for House of Commons elections in 2010–11. Under Alternative Vote, each voter lists the options in order of preference 1,2,3... If no option gains more than half of the vote, the option with fewest first preferences is eliminated, and those ballot papers are reassigned according to the second preference (if any) on each of them.

9. Whether or not AV would have been a good system for electing multiple candidates such as MPs (on which I express no opinion), it is a terrible system for any situation such as a referendum where a single option must be chosen, because it is not well-behaved as defined above.

10. It may fail to select a majority winner when one exists. This would be a fundamental violation of majority rule.

11. On the other hand, failure to put a “devolution-max” option up for voting might also lead to a perverse result. This may be illustrated from the history of the referendum on an Australian republic held in 1999.

12. Three options were being publicly discussed at the time: A: no change, Australia continues as a constitutional monarchy; B: Australia becomes a republic with its head of state chosen by both houses of Parliament; C: Australia becomes a republic with a directly elected head of state.

13. The only option that appeared on the ballot was B. It was defeated and the status quo A therefore remained.

14. However, robust poll evidence shows that the majority of Australian voters preferred C to both B and A. The referendum failed to choose the majority winner.

15. The decision to put only a single option up for voting probably had two motives, one sound and the other unsound. The sound reason is that multi-choice referenda are difficult to conduct and to interpret. The unsound reason is that Australian policy-makers assumed that the people of Australia would see B as intermediate between A and C. Therefore they assumed that public opinion would be single-peaked, with B being the option that nobody placed last. However, the monarchist campaign cleverly did not defend A but attacked B on the grounds that “you don’t want a bunch of politicians to choose your head of state, do you?”

16. I conclude that, PROVIDING that devolution-max can be defined to the satisfaction of the Electoral Commission, it would be desirable to have it as a ballot option.

17. This could be achieved by asking two questions independently (as in the Scottish referendum of 1997) or by putting both independence and devolution-max on the same ballot, but counting the votes by a well-behaved procedure.

18. Committee members will recall that in 1997 the ballot propositions were “I agree that there should be a Scottish Parliament” and “I agree that a Scottish Parliament should have tax-varying powers.” The result was Yes to both (74.3% of voters saying Yes to Q1 and 63.5% of voters saying Yes to Q2.)

19. The result was easy to interpret, as a Yes/No and a No/No result would equally have been. A No/Yes result might have seemed strange but would have been interpretable.

20. However, the procedure was not ideal even for the questions then on the ballot, because some voters did not have a straightforward choice: especially those voters who did not want a Scottish Parliament, but who thought that if the majority of voters supported it, it should have tax powers. It can be proved that this non-straightforwardness is an inescapable feature of a double-independent-question referendum such as that of 1997.

21. A more serious objection to copying the 1997 procedure is that, whereas in 1997 it was clear that a Yes/Yes implied support for a Parliament with tax powers, it is quite unclear what a Yes/Yes vote to both independence and devolution-max would imply.

22. The most difficult case, which is not at all unlikely, is a Yes to both independence and to devolution-max with the latter gaining higher support than the former. A Scottish government, if controlled by the SNP, would interpret such a result as a mandate for independence; a UK government would predictably resist that claim. Result, possible stalemate.

23. It is also unlikely that the Scottish and UK governments could come to an advance agreement on how to interpret such a result.

24. By elimination, therefore, I conclude that the best way to organise a referendum is by a single ballot in which voters are asked to rank both independence and devolution-max compared with the status quo. To the voter, the ballot paper would look identical to an AV ballot. The instructions to voters would state “please place a 1 against the option you most wish, and, if desired, a 2 against the option that is your second preference”. However, ballot papers which expressed only a first preference should still be treated as valid.

25. However, the counting procedure would be designed to find the majority winner by comparing A against B, A against C, and B against C. It would not be difficult to put this rule into Parliamentary language in a Bill or secondary legislation, nor would it be difficult to count, either by hand or with computer assistance. Such a procedure is known in the technical literature as a “Condorcet” procedure, after the Marquis de Condorcet (1743–94).

26. Nevertheless, the possibility of a cycle (see paragraph 7 above) always exists, however remote. Scottish opinion is probably single-peaked, but (as in Australia) policy-makers must not jump to such a conclusion prematurely.

27. The Bill (/statutory instrument) must therefore provide in advance for a cyclical outcome. The easiest solution would be, following parliamentary precedent, to say that in the event of a cycle the status quo prevails.

28. Everything in this note is based on the assumption that the questions to be asked, and any accompanying descriptions of the options, are subject to approval by the Electoral Commission, which I understand that both the Scottish and UK Governments accept should be the regulator of this referendum.

March 2012

Prepared 4th May 2012