How Might the US Presidential Election Have Turned Out Under Most-Least Voting?

My usual posts concern Best-Worst Scaling (BWS)[1] – a method of choices conducted at the level of the individual respondent to obtain his/her complete preferences. This leads to some heavy duty explanation about how we deal with the “within person variation” in such models. As an alternative “way in” to this field for newbies, I thought I’d discuss a simpler application of BWS, put forward by my co-author and voting expert Anthony Marley – Most-Least (M-L) voting[2] and how if used in the USA might have led to a different occupant of the White House.

With discussion (still) raging over possible foreign influence and whether Hillary Rodham Clinton might run again next time, I thought I’d take the discussion in a different direction. Would a very simple change to the US voting system (certainly in the primaries, potentially in the General Election) have given different candidates and ultimately President? I wish merely to stimulate discussion, as I necessarily rely on data not collected. But I intend to show how the use of Most-Least (M-L) voting automatically eliminates candidates who are extremist or engender hatred in large population subgroups.

Electoral reform is always a difficult subject. Arrow’s famous Impossibility Theorem[3] states that no ranked preference system of government can achieve all of a small number of commonly accepted “fairness criteria”. So, a country must decide what criteria are most important, then choose the voting system that best achieves these.

The USA, together with much of the Anglo-Saxon world, uses First-Past-The-Post with single member constituencies. This “winner-takes-all” method is simple, transparent and ensures everyone has a single representative (Senator/Congress member/MP etc) linked to their geographical area. However, in a multi-party world (or a two-party world with multiple factions), winners frequently obtain far less than 50% of the vote or win with low turnouts.

The Alternative Vote (AV)* system was put forward as a potential solution in a recent UK referendum – it lost. It was widely seen by its proponents, the Liberal Democratic Party, to be a “stepping stone” to a fully proportional system. It retains many FPTP benefits in terms of constituency links with a single representative. It differs in that the voter ranks the candidates/parties. If no candidate achieves a win (50%+1 votes) in counting first rank votes, the candidate with the smallest number is eliminated and their second preferences are redistributed among the rest. This continues until a winner emerges.

AV sounds attractive. In practice it has engendered anger in Australia, which uses it. The instant run-off nature allows eliminated candidates “another bite at the cherry” whilst the combination with proportional representation in the Senate allowed a member of the “sports party” to be elected in Western Australia with a primary vote of 0.2%. Why is it problematic? This goes to the heart of a proposed solution – Most-Least (M-L) voting.

Most-Least voting recognises that people are good at identifying the candidate they like most, and the one they like least. However, it has long been known that middle rankings are frequently unstable – in practice people often put all the remaining items in a list in arbitrarily. Furthermore, eliminated candidates should not get “more bites of the cherry” by having multiple rankings contribute to scoring – indeed in a world of proliferating extremism it can be argued that those endorsing such policies should get an equal but negative bite at the cherry!

M-L, therefore is a simple extension to FPTP. “Most preferred” voting and counting is conducted as now. However, every voter must also indicate the candidate they like least for their ballot to be valid. Least totals for all candidates are calculated, then subtracted from the most totals. The candidate with the highest net-most-minus-least count wins.

How might this have played out in the US Primaries?

Well the Republican primaries would almost certainly have eliminated the current President, Donald Trump. Let’s assume for the sake of argument that in a given state he could count on 40% support with around 10 competing candidates, most of whom were from “the establishment” and loathed him. In the extreme case of all their voters using their “least” choices against him, his net score would have been minus 20% (40-60). Meanwhile there is only “his” 40% of least choices to try to knock out all his opponents – impossible.

What about on the Democratic side? Of course Iowa was the only State with the necessary 3+ candidates for M-L to be usable, but everything might have gone differently using the method. Clinton and Sanders virtually tied in “Most” votes, with O-Malley getting only 0.5%, leading to his withdrawal. But what might have happened if “Least” voting had been used too? If supporters of Clinton and Sanders loathed each other, it’s not inconceivable that they would have knocked each other out, leading O’Malley to win by a whisker! In any case the two leading candidates would have had to do fancy footwork to ensure they didn’t put off too large a segment of their opponent’s constituency – a tough task for Clinton in particular given the large levels of antipathy toward her.

This considers the Primaries. Voting at the General Election would need some large constitutional changes to use M-L. However, it is interesting to consider how it might solve a lot of the logjam in Washington DC. M-L voting encourages third parties: Democrats and Republicans in many competitive and potentially competitive seats could easily knock each other out, letting a third party candidate come through the middle – someone who doesn’t alienate large numbers of voters (but who equally might not enthuse large numbers either). Those legislators perceived to be contributing to the logjam in Congress might be in trouble if their competitors “gang up on them” in terms of least voting.

However, returning to Arrow, does the USA want to eliminate the radicals? You might end up with a Congress of “nobodies”. But it certainly provides food for thought.


1. Best-Worst Scaling: Theory, Methods and Applications. Louviere JJ, Flynn TN, Marley AAJ (2015). Cambridge University Press.
2. Characterizing best-worst voting systems in the scoring context. García-Lapresta JL , Marley AAJ Martínez-Panero M. Social Choice and Welfare 34(3): 487-496
3. Arrow, Kenneth J. (1950). “A Difficulty in the Concept of Social Welfare” (PDF). Journal of Political Economy. 58 (4): 328–346. JSTOR 1828886.doi:10.1086/256963. Archived from the original (PDF) on 2011-07-20.

* Naming differs in some references depending on how eliminated candidates’ ranking data are dealt with