Alternative alternative voting systems, part four: TMPR

TMPR stands for ‘Two-member proportional run-off’. This is another method that I’ve invented, in the wake of ARV, which I discussed in the last post in this series.

TMPR is a blend of, and compromise between, the UK’s present single-member, highest-plurality system (First Past the Post – FPTP); an instant run-off, majority system such as the Alternative Vote (AV); and a multi-member proportional system such as the Single Transferable Vote (STV). It contains enough of what’s good about each of these systems to offset what’s bad about them, which I aim to bring out in my detailed analysis below. So TMPR ought to satisfy proponents of each, although – like compromises in general – it may end up satisfying no one.

TMPR offers all of the following benefits to some degree:

  • It’s crudely proportional
  • It preserves the close link between an MP and his or her constituency
  • It would largely eliminate ‘safe’ seats
  • It would ensure that the great majority – i.e. significantly more than 50% – of constituents have at least one MP they’ve voted for as their first preference or, if not, as a second preference, making parliament much more representative of voters
  • It respects the majority and, failing that, highest-plurality principles
  • It gives voters the option to vote for their genuinely preferred party as well as exercising a tactical vote
  • It would give the smaller parties a much greater chance of making a break-through than FPTP or AV
  • And it would be easy for voters to understand what to do and how to get the most out of the system.

This is how the system works:

  • There are two seats per constituency: larger two-member constituencies would need to be formed by merging two existing adjacent single-member constituencies (with allowance being made for proposed boundary changes, so as to ensure that the constituencies all had roughly the same population size)
  • Parties can field two candidates, who are numbered one and two on the ballot paper
  • Voters have a first- and second-preference vote, which they must use for different parties; they can limit their vote to only a first preference, if they wish. Votes are for parties, not individual candidates: each party’s candidates and the order they appear in the ballot paper (1 and 2) are determined by open primaries, so that voters have already been involved in selecting the individual candidates before the election
  • Any party gaining over 50% of first preferences automatically wins both seats: candidates 1 and 2
  • Any party gaining over 1/3 of first preferences but not more than 50% automatically wins one seat: this goes to the No. 1 candidate for that party
  • If two parties gain over 1/3 of the vote but neither wins over 50%, they each gain one seat, and that is the end of the election: these seats go to each party’s No. 1 candidate
  • However, if no party or only one party gains over 1/3 of the vote, all the parties remaining in the race (obtaining exactly 1/3 of the vote or less) enter an instant run-off
  • This works by adding the second preferences of all voters – including those who’ve indicated the party that has already succeeded in obtaining over a 1/3 of the vote, if that is the case – to the first preferences
  • If one party has already won a seat and obtains over 50% of the combined total of first and second preference votes after the run-off, it wins both seats. Similarly, if no party has won a seat on the first-preference votes but one party obtains over 50% of the combined total of first and second preference votes after the run-off, it wins both seats
  • Otherwise, the winner of the outstanding seat (or seats, if two are still available) is simply the party (or parties) that obtain(s) the highest total (and second-highest total, if two seats are still being contested) of combined first and second preferences.

I’ll discuss the principles behind these features of TMPR as I proceed with my analysis of its merits based on the criteria I’ve used to rate other systems, including FPTP and AV, in previous posts in this series.

My first criterion is: Does every vote count / is every vote counted? With TMPR, as in all forms of instant run-off voting (IRV), you can get a situation where some of the votes are ‘not counted’ and therefore don’t count towards the final result: second-preference votes that are not needed to produce the final result, i.e. where two parties have already won the seats available based on first preferences. However, unlike AV, it is quite simple to include the second preferences in the presentation of the election results, even if those preferences haven’t been used, whereas it’s not the proposal, under AV, to publish the totals of all the preferences for all the parties.

Providing the totals of first- and second-preference votes would enable people to compare the results for when only first preferences are counted with those when you combine them with second preferences. This would provide valuable information for analysing patterns of tactical voting and the degree to which voters for larger parties also support the smaller parties (by voting for them as their second choice), and vice-versa: the ways in which voters for the smaller parties switch their allegiance to the larger parties in their second preferences. This relates to the discussion below about the extent to which TMPR would enable voters to send a message to politicians.

The question, ‘Does every vote count?’, mainly implies ‘are there any wasted votes under TMPR?’; i.e. does every vote count towards the final result? Well, one significant advantage of TMPR over AV is that the run-off uses the second preferences of all voters to determine the result, and not just the second and subsequent preferences of a greater or smaller minority of voters, as in AV. This is fairer and more consistent.

In addition, a greater proportion of voters’ first preferences influence the result than under FPTP and AV. For a start, a party needs to obtain only over one-third of first preferences to be guaranteed a seat; and if two parties cross this threshold without obtaining more than half of the vote, this means that over two-thirds of voters’ first preferences have been used to determine the winners of the election. If one party does gain over 50% of first preferences, this still means that the very minimum quota of first preferences that can influence the result is 50% plus one vote. This is in contrast to AV, where – despite what is generally said – the winner can still obtain the support of only a minority of voters, and even then, this is only on the basis of votes transferred from other parties.

Then, if second preferences come into play, this means that the votes of an even broader cross-section of the electorate are involved in shaping the result. One of the reasons for allowing second-preference votes for a party that has already secured one seat (by winning over 1/3 of first preferences) to enable that party in theory to win over 50% of combined first and second preferences (and thereby win both seats) is to provide an extra incentive for voters to use their second preferences for other parties. Otherwise, voters who had awarded their first preference to the party likely to finish second in the ballot (e.g. Labour) might be tempted to ‘bullet vote’, i.e. not indicate a second preference in case that damaged the prospects of their first preference in the run-off. However, as that could run the risk of allowing the leading party (e.g. the Tories) to win both seats (for instance, by capitalising on second-preference support from Lib Dem voters), voters of this sort would have a motivation for using their second preference, even if this were for a party that did not stand a chance of catching up with their first-preference party (e.g. the Greens). You could call this a ‘wasted vote’; but those votes could in fact be for minor parties that such voters genuinely sympathised with, and this mechanism would then provide a means to boost the support that minor parties receive.

So, for a combination of these factors, I’d award TMPR four points out of five for this criterion: in the absence of a clear overall majority for one party, a much higher proportion of votes are involved in determining the winners than under AV or FPTP. But there are still some votes that are not involved in determining the result.

In terms of my second criterion, is the system proportional?, I’d award TMPR three points out of five. This relatively mediocre score is despite the fact that, unlike all the single-member systems I’ve discussed up to now in this series, TMPR is proportional in its actual design. That is to say, the rationale for allowing parties to win one seat once they cross the threshold of 1/3 of the vote is that this figure represents the minimum proportional ‘quota’ required to qualify for one seat in a two-party constituency – on the basis that no more than two parties can obtain over 1/3 of the total vote. This is the same principle that is used in multi-member STV: in a four-seat constituency, the quota for a candidate to win a seat is one-fifth plus one vote.

To be logically consistent and fully proportional, TMPR ought to stipulate that, in order to win both seats being contested, a party would need to obtain two-thirds of the vote plus one vote rather than 50% plus one. However, the purpose behind allowing parties to claim both seats if they obtain over 50% support is to make TMPR more like a single-member majority system, and to provide an extra incentive for parties to go out and try to win both seats in areas where they’ve traditionally enjoyed majority support, e.g. Labour in the North of England and Scotland, and the Tories in southern England. This feature ought to make TMPR much more acceptable to those parties, given that around one-third of the current crop of MPs obtained the support of a majority of their constituents at the last election, and the constituencies involved are often concentrated in particular urban or rural areas. Therefore, amalgamating such seats into two-member constituencies, and allowing those constituencies to return two MPs from the same party if that party wins over half of the votes, should not affect the representation of that party in those areas too adversely. However, that’s without taking into consideration any change in voter behaviour that TMPR might produce, such as a greater willingness to vote for minor parties as a first preference.

Even so, TMPR is still more proportional than FPTP or AV, in that, in the absence of an overall majority, it awards one seat to each of the top-two parties in a constituency; and it makes sure that, in order to win both seats, a party must obtain the support of over 50% of voters. TMPR would be likely to generate a significantly larger (and hence, more proportional) number of Lib Dem MPs than either FPTP or AV, whether on the basis of first-preference votes (particularly in the southern half of England) or with the aid of second preferences (in the Midlands and the North of England). In the North and Midlands, there would also be lots of seats returning one Labour and one Tory MP.

In addition, as I stated above, TMPR would give minor parties more of a chance than FPTP and AV. This is because the minimum barrier to win one seat (one-third of the vote plus one vote) is lower than under AV and, typically, FPTP; and because smaller parties stand to gain more second-preference votes from people whose first preference was for one of the three main parties: particularly, where those voters do not wish to provide an advantage for one of the other larger parties by either not using their second preference at all or by giving it to another of the larger parties – but also, if voters genuinely want to show support for one of the minor parties. In this way, you could expect UKIP, for instance, to pick up a lot of second preferences from Tory first-preference voters, and the Greens to similarly gain backing from Lib Dem and Labour first-choice voters. By contrast, under AV, the subsequent preferences of Tory, Lib Dem and Labour voters for those smaller parties will generally not be counted at all, because by the time votes for the major parties are transferred, if they are at all, to another party in an AV election, UKIP and the Greens will already have been eliminated.

All the same, TMPR is a cruder and less granular form of PR than STV, in that the fewer seats are available per constituency, the more the overall result deviates from pure proportionality – as well as because of the 50% rule. Hence, as I would probably award STV four out of five for proportionality, I have to give TMPR only three out five.

With respect to my third criterion, Does the system foster accountability?, I’d give TMPR four out of five. One of the effects of TMPR would be to greatly reduce the number of ‘safe seats’. This is not just because it reduces the number of seats that Labour and the Tories can win on a plurality of the vote (because a plurality of over 33.33% wins you only one out of every two available seats, not both seats as is effectively possible under FPTP) but also because of the system of open primaries. Under TMPR, MPs and candidates from other parties would be obliged to submit themselves for (re-)selection before every election. In addition to determining whether the incumbent MP would be allowed to run again, these open primaries would also determine in which order that MP would appear in the ballot paper for their party, i.e. No. 1 or No. 2. In a constituency where the MP’s party had not obtained over 50% of the vote at the previous election, being listed No. 2 could be tantamount to de-selection, given that only the No. 1 candidate is elected when parties obtain between one-third and a half of the vote.

The point of these open primaries is partly to increase the accountability of MPs to their constituents during their incumbency as well as at election time. But this is also to allow voters the chance to select individual candidates rather than just vote for a party, which is what they do under TMPR at the election. The reason why TMPR does not allow voters to vote for individual candidates – except if parties field only one candidate – is that this prevents the election from degenerating into a highly complex series of tactical calculations (such as one party fielding only one candidate in order not to dilute its vote, to the disadvantage of a more popular party fielding two candidates) and makes it less likely that complicated run-offs are required, as many elections are capable of being decided clearly and fairly based on first preferences alone. Having open primaries compensates for this by allowing voters to pick individual candidates.

In the open primaries, all registered voters would be entitled to be involved in picking the candidates each party would field at the next election. The only voters excluded from the primary poll would be members of other parties. This system would result in virtually no MP feeling totally safe that they could be re-elected time after time. In addition, as the overall election result would be more proportional than single-member systems, parliament as a whole would be more accountable to the total electorate.

What about independent, i.e. non-party, candidates? Well, as in the case of parties fielding only one candidate, independent candidates would have to obtain over one-third of the vote to be elected. If, by some freak, an independent candidate won over half of the vote, they could by definition take up only one seat. So the other seat would be awarded to the party obtaining over 1/3 of the vote or, in the absence of that, a run-off would be held in the usual manner.

Criterion No. 4: Does the voting system allow voters to express the full range of their political and personal preferences, and send a message to politicians? When discussing my first criterion (does every vote count?) above, I argued that counting the first and second preferences of all voters would empower voters to use their vote to let politicians know what they think about them – e.g. by voting for a minor party as a first or second preference (whether out of conviction or as a protest vote). In addition, TMPR significantly lowers the risk barrier to voting for a smaller party out of conviction, as this is less likely to damage the prospects of the party for which you usually tactically vote, given that that party needs to secure only one-third of the vote to win one seat – and you can help them do so with your second preference, if that is needed.

Similarly, as I discussed in connection with my second criterion – proportionality – above, the incentive that TMPR creates to use your second-preference vote in such a way as to disadvantage parties you do not support means that many voters will vote for smaller parties that they genuinely sympathise with as their second preference, albeit also out of tactical considerations. TMPR therefore encourages voters to express both a conviction vote and a tactical vote, and their first and second preferences are more likely to genuinely coincide with their actual first and second preferences, albeit that the party they ‘like’ the most might be indicated as their No. 2 choice, depending on whether voters decide to list either their conviction vote, pragmatic vote or indeed protest vote as their No. 1 choice. So, for this criterion, I again award TMPR four out of five: voters can vote for their two most strongly supported parties, and those votes can both be influential in determining the result while also sending a message to the politicians.

The ability for people to vote tactically as well as out of conviction or protest means that I can give TMPR only three points out of five against my fifth criterion, Does the system mitigate the need to vote tactically? It is true that voters are not obliged to vote only in a tactical manner, as they so often are under FPTP. But there are some tactical calculations that can be made, such as whether and for which party to use one’s second-preference vote so as not to be detrimental to one’s first-preference party. However, there’s only a limited extent to which tactical strategies can actually come off, in that parties whose defeat you might wish to ensure will usually need to win only one-third of the vote plus one vote, and if they do so, there’s nothing much anyone else can do about it.

Finally, my sixth criterion: how easy is the system for voters to understand, trust and use effectively? Here, I’d give TMPR four out of five. Admittedly, it’s a little more complicated than FPTP, to which I gave three points out of five against this criterion. However, in essence, TMPR is pretty straightforward: voters just have to indicate a first and second preference. And it would be easy for voters to work out how to use their preferences to best advantage to try to secure the outcome they most desire, whether that’s both seats being won by the party of their choice (bullet vote just for that party); one seat won by party A and the other by party B (vote for party A as your first choice and B as your second, or vice-versa); or making a protest vote (vote for the party representing your protest as your first preference and then your usual party as your second); etc. I think voters would also realise TMPR is much fairer, in that if two parties obtain between one-third and half of the vote, they both win a seat.

So how does TMPR compare against the single-member systems I’ve discussed thus far? In the table below, I’ve compared the scores I’ve just awarded to TMPR with those for the other systems:

Criterion FPTP AV AppV ARV TMPR
Does every vote count?

3

2

3

4

4

Is the system proportional?

1

2

2

3

3

Does the system foster accountability?

3

3

4

4

4

Does the system let voters express their views?

1

2

3

4

4

Does the system mitigate tactical voting?

1

2

2

3

4

How user-friendly is the system?

3

2

4

3

3

Total scored out of a maximum of 30

12

13

18

21

22

TMPR emerges as the best of the systems discussed in this series to date – admittedly, only by reference to my own criteria and with scores that some would dispute. I’m aware it could seem highly vain to award the largest number of points to the two systems I myself have invented (ARV and TMPR). But I’d love it if readers would take issue with any of the detailed points I make in connection with aspects of each system or with the criteria I’m using to assess them; rather than purely taking issue with the system itself in relation to more technical mathematical-probability calculations or the many specialist technical criteria for assessing voting systems. If I’m wrong to consider that TMPR has the advantages I ascribe to it, then please take me to task on them.

But for now, I hold to the view that TMPR is an excellent compromise between the best of FPTP, AV and STV, the latter of which I haven’t yet discussed. I was originally planning to discuss the AV+ system for the present post in this series. But then I had the brainwave of TMPR, which I was keen to discuss first. So – barring any further brainwaves – it’ll be AV+ next time.

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7 Responses

  1. […] FPTP results are distorted by tactical voting. These problems do not exist in either of the ARV or TMPR voting systems discussed in previous posts: ARV always awards the win to the most popular candidate […]

  2. // Triple(Cumulative)–Transferable–Vote //
    The Ballot paper lists candidates individually, and asks you to allocate the ranks one-to-nine, but you may allocate up to three different ranks to any one candidate. The first three positions will be counted as votes for the initial count, at the end of which the most lacking candidate will be eliminated, and his/her votes transferred… (pretty much as per STV). The cycle will continue until two candidates are elected, each with at least a third of the vote.

    // Double-Member-Constituency Weighting //
    With each constituency electing two MP, who will actively compete and provide comparison throughout the parliament with a collective support of more than two thirds of the electorate; there is a platform in which to ‘weight’ support without creating a disparity between the power of different constituencies. Parliamentary votes will be determined not simply by the number of members voting for and against, but by adding up the corresponding point values that each MP has received in the election. After MPs are elected, the ballot papers will be re-interpreted in a Borda Count covering the two MPs: Each ranking position is allocated a value in points to be accumulated (1st=12 points, then -1 point per rank). The point scores of the two candidates will give the ratio at which the constituency’s support is to be distributed. This per-constituency weight will be 100 for average size, varying by proportianlity of the 0.9 power of population, between 80 and 120. This will provide real-terms proportionality for the parliament, while retaining individual accountablity and creating even more equal counry-wide representation. The ‘weight’ value has potential to be used in determining other things, such as ministerial eligibility and MPs salaries.

    // Executive Elections //
    In a Hung Parliament, it will not be at the discretion of a third or fourth party which direction the country takes, and instead there will be an accountable format for the negotiations and outcome. A Second Polling day will be declared, where there are two candidates: each a proposed working majority, generally one led by each of the two largest parties. Parties will have until a week before this election to negotiate what these two proposals will be and launch official agreements/manifestos. Parties will be able to associate themselves with both proposed ‘deals’, but must officially declare only one in which they will be able to serve ministerial roles, so that there is no guaranteed assumption of office. The two-way executive election will then return a democratically sound Government and parliamentary layout.

    … I could argue all the positives for ages, but you seem able to anayse it well yourself. I’d say it scores 3 on all three criteria, probably bar the lesser and patronising one in my view, and also introduced further positives you may never have even considered.

  3. I do indeed take issue with some of the rankings of the systems you’ve invented.

    First off, both of them are complicated. You thought of them, so of course they seem clear to you, but anything that takes you paragraphs to explain is not actually simple.

    Secondly, some of the complications seem totally unnecessary. For instance, why would anyone neglect to vote at least one “5” in ARV? Aside from a purely-symbolic protest vote, the only possible effect would be to allow your voice to be more-easily overwhelmed and get a winner you like less. Similarly, the “all second-choice votes count” provision in TMPR would just make the major parties found shadow parties so that they could win both seats with 34% (as long as the opposition remained divided).

    Third, both of them encourage tactical voting more than you realize.

    ARV has essentially two strategy equilibria: strategic approval voting for a majority winner, if there are one or two clear frontrunner parties; or range voting for a minority winner – which also strategically reduces to approval voting – if there are 3 or more strong parties. In the former case you’d be strongly forced to choose a “lesser evil” from among the frontrunners; in the latter case, you’d be weakly pushed towards a range-style vote, in order to have the most power in the races that count. So, at best, it’s as strategic as AppV; and yet that strategy analysis is more of a headache, so I’d actually give it fewer points.

    As for TMPR, it’s a strategy nightmare. What if you prefer, say, greens over labour over others, in a labour-strong constituency? If you vote for labour with either your first or second vote, you may put them over 50%, and take the seat from the green; but if you and 17% of voters like you don’t vote for labour, they may not even get a seat. I could go on; the point is that, the more complicated the system (trying to be proportional, yet save “safe seats”, yet foster the growth of the smallest parties, yet…) the more strategic opportunities arise.

    Consistent with your first three columns, I’d rate your two systems
    Does every vote count?
    3
    2
    3
    3
    3
    Is the system proportional?
    1
    2
    2
    2
    3
    Does the system foster accountability?
    2 (I downranked FPTP for “safe seats” and Duverger’s law)
    3
    4
    4
    3 (incumbents in split-party constituencies could sail through the primaries and easily pass 1/3)
    Does the system let voters express their views?
    1
    2
    3
    4
    3
    Does the system mitigate tactical voting?
    1
    2
    2
    2
    2
    How user-friendly is the system?
    3
    2
    4
    2
    2
    Total scored out of a maximum of 30
    12
    13
    18
    17
    16

    So, both of your methods are better than FPTP and AV, but worse than AppV.

    However, if you like ARV, you should definitely look into MCA (2-rank Bucklin). As I describe in response to your first post in the series, it’s just Approval with an extra “preferred” rank; if anyone gets over 50% “preferred”, they win, otherwise preferred counts as approved and you use Approval. If there are multiple majorities in approval – say, 52% and 58% – the one with more preferred votes wins; that encourages those preferring strong candidates not to be to stingy with their approvals. It’s similar to your ARV, but simpler (obviously) and less tactical (because if there’s no top-ranked majority, the second-rank votes count with full tactical strength, as you’d want them to.)

  4. typo: I meant “too stingy”, not “to stingy”.

  5. […] Proportional Represenation (version two). This is a simpler and more practical version of the TMPR system I have previously discussed. TMPR2 works as […]

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