Multiple Choice Voting systems

So as the rerun of the referendum becomes more likely, some people are considering a multiple choice; the problem is how to weight and count the votes. It’s interests me that instant run off is people’s first port of call, and I have some links that refer to it. To me, the problem is that instant run off fails to weight people’s commitment to their 1st vs. 2nd choice. This problem is what Parliaments are designed to solve; the polity can negotiate 1st, 2nd and 3rd choices and negotiate the importance of each packages features, this may be impossible in an instant run-off election. I have written more …

It seems that political scientists and mathematicians study this problem in some detail and have developed some principles to guide in voting systems design. At the moment the best I have found is on Wikipedia, instant run off voting, where its voting method criteria section lists these criteria. I am not sure if the criteria spoken about take into account motivational effects which are impossible to eliminate; how do we eliminate the motivational effect of Scottish independence i.e. where people vote leave because they expect it to accelerate Scottish independence.  Neither is it immune to tactical voting strategies. Possibly most importantly, the Condorcet majority principle , together with participation and reverse symmetry criterion are not met.

The Condorcet candidate ( a.k.a. Condorcet winner) is the person who would win a two-candidate election against each of the other candidates in a plurality vote. … A voting system satisfies the Condorcet criterion (English: /kɒndɔːrˈseɪ/) if it always chooses the Condorcet winner when one exists.

The wikipedia page identifies 12 qualities of a voting system,and suggests that instant run off systems satisfy six and fail six. I am unsure why I only identified three failures, i.e, the Condorcet majority principle , and participation and reverse symmetry criteria. Each oh these qualities has it’s own page.

I have found wikipedia very useful, often, as a start point.

I have found these links which are much lighter, as in not written by mathematicians.

  1. Beyond the binary: what might a multiple-choice EU referendum have looked like?, from Democratic Audit, an examination of how the ballot paper might look but no discussion on how to mark or count the votes.
  2. A paper to Labour’s NPF, An introduction to the idea of a three-option Brexit referendum by Nick Donovan, catalogues the 19 such referendums that have occurred.
  3. A second Brexit referendum: the practical questions, at the Institute for Govt, written in July 2018, looks at the choice,the voting system, the victory threshold (in terms of devolved nation consent) and the franchise by Akash Paun.

These are a bit more scientific

  1. Beyond instant runoff: A better way to conduct multi-candidate elections, by Christopher Borgers at the Examine’s instant run off, the Condorcet rulesand looks at the Borda count system of weighted votes, and describes results propensity of the two systems and games to be played.
  2. Borda Count, at the ERS, a weighted preference vote, like that used in the Eurovision, mainly descriptive.

Some further reading, from wikipedia;s sources,

  1. Four Condorcet-Hare Hybrid Methods for Single-Winner Elections
  2. Range Voting and the Mathematics of Democracy, includes a fascinating example where each voting system produces a different vote, written by Warren D Smith, founder of the centre for range voting who argues that range voting is best.
  3. Point/Counterpoint: Terry Bouricious Attempts To Rip Professor Gierzynski A New One Over Instant Runoff Voting Controversy (Now With All New Gierzynski Update!), a serious row about the advantages and disadvantages of instant run-off.

Late browsing of the wikipedia sources list led me to this,

  1. Arrow’s impossibility theorem, which poses an impossible trilemma, based on trading th accuracy of the voting system and the representative nature.


Image Credit: SMARTBOY10 VIA GETTY IMAGES, found at Huffpo, cropped, and stored for the usual reasons

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