Is free-list PR a “simple” electoral system?

This seems like a trick question. Of course, free-list has all sorts of complex features. In such a system, the typical rules are that any voter may vote for as many candidates as he or she wishes, even across different lists (panachage). A vote for any candidate on a list counts as a vote for that list for purposes of determining proportional seat allocation across lists, as well as for the candidate in competition among other candidates on that list.

However, this system handles votes and seats for lists just like any other list-PR system: It is designed to allocate seats to lists first, and only then to candidates. It thus is “simple” on the inter-party dimension, unlike SNTV or MNTV or STV (where candidate votes do not count towards aggregate party vote totals and seats are allocated based only on candidate votes).

My general definition of a “simple” electoral system is one that is a single-tier, single-round, party-vote system. The free-list could be said to violate that last part of the definition, in that “party vote” maybe should mean a single party vote per voter. My instinct is to keep free list in, because it remains “simple” in terms of how it processes the votes across lists. But I could be convinced otherwise, given that effectively every voter can vote for more than one list–a “dividual vote” in Gallagher’s terms.1

In Votes from Seats, Taagepera and I kept at least three free-list systems in our dataset: Honduras (since 2005), Luxembourg, and Switzerland. The issue came back to my mind because of my consideration of including some smaller countries and non-independent territories in a dataset for some further analysis of key questions. One of the smaller countries that could be added to the data is Liechtenstein, which I believe uses a free-list PR system. My gut says “yes, include” but now I wonder if we already violated our own criteria2 in having those free-list systems in the prior analysis. To be clear, none of our results would be changed if we had dropped them.3 It is just a matter of consistency of criteria.

Questions like this always nag comparative analysis, or science more generally. What things are part of the set being analyzed? It is not always clear-cut.


  1. Note that there is no question regarding standard open-list PR: Even if there are multiple candidate preference votes cast per voter, as in Peru, only a single list vote is registered per voter.
  2. In fact, on p. 31 of Votes from Seats, we say “Only categorical ballots and a single round of voting are simple, by our definition.” A free-list ballot is dividual and thus not categorical. However, the reason we give for limiting the coverage to categorical ballots is that “other ballot formats… may violate a basic criterion for simplicity in the translation of votes into seats: the rank-size principle” (emphasis in original). For example, the party with the most aggregate votes in a district may not have the most seats allocated in the district (or at least tied for most with the second-most voted party). This violation of the rank-size principle can occur with SNTV, STV, and MNTV, but as noted above it can’t occur in free-list PR (per my understanding, anyway). I note that in a later work, Party Personnel, my coauthors and I seem to adopt a stricter definition. On p. 53 of that book, we say that simple means “a voter votes once, and this vote counts for the entire party list of candidates.” Yet the conceptual point there is somewhat different, in that we are referring to “simple vote” not simple electoral system, and we remove open-list PR from the standard of simple vote because they permit differentiation of candidates within a list in the same district. But as for the vote counting for the entire list, free list still meets that part of the criterion. (A reminder that “voting system” is not a synonym for “electoral system”!)
  3. Although I did not think of this possible issue with free lists at the time, I definitely ran robustness-check regressions with Switzerland dropped. I did so mainly because of its multiparty alliance feature, which also is a complex feature for reasons discussed in the book (mainly with reference to Finland and Chile). Doing so did not affect the results, so we left the case in. There are not enough elections from the other free-list cases, nor are they observably different on our outcomes of interest, that they could affect results. (Switzerland is observably different–far more fragmented than expected for its seat product, and that seems to be mostly due to alliances, even above the impact of its ethnic fragmentation–see p. 269 of Votes from Seats. But the inclusion or exclusion fo the case is immaterial for the overall results.)

21 thoughts on “Is free-list PR a “simple” electoral system?

  1. I guess I won’t weigh in on your question–is it simple?–only because I don’t understand your purpose well enough. Still, using your general definition above–which focuses first on how the system “handles” votes wrt seat allocation, and second on the “single-tier, single-round, party-vote” features–a few reactions that may cut against your definition…
    First, the free list CAN “handle” votes for the seat allocation process in a simple way, but it DOESN’T NECESSARILY do so. In our 2018 ES paper, John and I find a few cases that “weight” the invidual votes cast by individual voters in order to compensate for a tendency to cast fewer votes than permitted (usually, fewer than M). So for example, if you and I have 2 votes, but I cast two and you cast 1, they would weight your vote 2x to make you whole. El Salvador 2015 used weights at the individual level, and Ecuador 2006 used weights at the district level. Does that count as simple?
    Second, it’s true that within the district, and with respect to seat allocation, they are allocated to list first, then candidate. But any effort to generalize between districts of different sizes calls for some kind of mechanism to weight districts with different M. For example, the Swiss Federal Statistical Office devised of “fictitious voters” to make statements about the national strength of parties. How would this kind of operation figure into your definition of “simple”?
    Lastly, Ecuador from 2006-2017 was a case where it was free list with multiple tiers. One ballot distributed seats for the provintial deputies, and another for the national deputies. My point is simply that a free list can violate other features of your “simple” set, even before considering the party-vote.

    Liked by 1 person

    • I likewise am curious about the purpose for classifying free list as simple or not — from what I understand, it certainly seems like it could.

      One thing I wonder, which may or may not factor into this question — how often do voters in free list systems cast preferences across parties? That seems to be the real differentiator between free and open lists. If voters aren’t casting preferences across parties, I would wonder why (cognitive demands? Ballot confusion), and then also wonder whether the extra “complexity” of free list is worthwhile. I note “complexity” in quotes because I think free list can really be a very straightforward and appealing system, if designed carefully — though I’m not sure I would describe any of the existing examples as such.


      • Cognitive demands, maybe, or just not caring. I keep coming back to the fact that, in Australia, STV ticket voting hovers around 90%… or that, in the US, very much work is undertaken to get voters to use rankings. Whatever the reason, I’d also like to see the data you mention.


      • I don’t wish to speak for Matthew but I think the ‘simple’ classification here is to do with the Seat Product Model. A ‘simple’ system is one without any need to consider aggregation across districts or multiple rounds as additional factors. It’s not necessarily a reflection of how voters interact with the system.


      • On the system, and cognitive demands, pre Jack’s comment, I do not think the Australia (Senate) analogy works here. In that case, it is very easy to just cast a ticket vote and very onerous to cast a ranked-choice vote (at least before the changes in 2016 or thereabouts). So, of course, most voters take the less demanding option.

        With free list, there may not be an easy way to cast a single list vote (although there also may be, depending on ballot design), but it is very easy to cast a cross-party vote, where that could just be “I like this candidate here and this other one there, and I am done.” That is, a voter can partially abstain, while still engaging in cross-party voting, and the vote is valid.

        (It is even easier if there is cumulation: I will cast x-1 of my votes for my favorite candidate in the party I like, and 1 for this interesting candidate in this other party. Still pretty easy for the voter.)

        As far as the data, it can be estimated, but my understanding is that the electoral authorities in the countries in question do not publish data specifically on split-ticket voting.


    • What Henry said.

      That is, I accept that the system itself is complex. Is it so complex that we would not expect the Seat Product Model to apply? It depends on how we conceptualize the system and how much we re-interpret or modify our existing definition of “simple” electoral system.

      And it may be that it is outside the definition, but still functions as if simple. That is true for Australia and Ireland, for example. Clearly they do not meet our definition, but in Chapter 16 of Votes from Seats we show that their outputs are almost identical to what we would expect from the SPM if Australia’s house were elected by FPTP and Ireland’s by list PR (with all other parameters staying as they are). Even for France, the average outcome in seats is pretty close to FPTP expectations for that large an assembly (but for votes, not so much).

      As I mention in footnote 3, we already included Switzerland, and its results are somewhat anomalous. It is not clear if that is due to the free list or other factors.

      So the discussion is entirely about case-selection criteria, and not a statement about the electoral system, per se.


  2. Somewhat off-topic, but I just ran across a major example of violation of the rank-size principle: Kosovo in 2021!

    It is a single district of 120 seats, but per Wikipedia:

    The Assembly had [under the Constitutional Framework] 120 members elected for a three-year term: 100 members elected by proportional representation, and 20 members representing national minorities (10 Serbian, 4 Roma, Ashkali and Egyptian, 3 Bosniak, 2 Turkish and 1 Gorani). Under the new Constitution of 2008, the guaranteed seats for Serbs and other minorities remains the same, but in addition they may gain extra seats according to their share of the vote.

    The result of this is that there are parties with as much as 2.5% of the votes but no seats (there is also a 5% legal threshold for non-ethnic parties), and parties with as little as 0.14% who have seats when somewhat larger ethnic parties do not. For instance, the United Roma Party of Kosovo has a seat with 1,208 votes while the Innovative Turkish Party, with 1,243 votes, has none.

    In addition, these provisions result in the odd case of a party with a majority of the vote not getting a majority of the seats, which is certainly unusual for a proportional representation system!


  3. Back on topic, it seems Liechtenstein indeed uses free-list PR. Thanks to John Polga-Hecimovich (personal communication) for sending a link from a government web page, which says, in part:

    In parliamentary elections, Liechtensteiners cast two set of votes. Votes are cast for parties, and votes are cast for particular candidates. Depending on where one lives, each voter has 10 (Lower Country) party votes, or 15 (Upper Country) party votes. In addition, each voter can cast their respective 10 or 15 votes for various members of Parliament. The composition of seats in the Parliament is decided by the party votes, and depending on how many seats a party gets, the candidates with the most votes get a seat in the Parliament. 15 members of Parliament are from the Upper Country, 10 from the Lower Country.

    I am not sure this resolves my question about simplicity or not, however. It is good (for my purposes) that the candidate votes are separate from the party votes, so we know a voter actually intended to vote for a given party, rather than just somewhat randomly liking one or more of its candidates. But the system explicitly gives the voter multiple party votes. That is wild!


    • Also not clear is whether a voter can cast only party votes or only candidate votes, or some mix. And can they cumulate? For instance, if I just want to endorse one party list in its entirety in Upper Country, can I cast 15 party votes for it?


      • Indeed. I suppose I can understand giving voters multiple (10 or 15) candidate votes, but why also give them the same number of party votes? Seems unwieldy, and that the complexity would outweigh any benefit, but perhaps I’m missing something.


  4. Pingback: Kosovo 2021: A single-district electoral system that violates the rank-size principle | Fruits and Votes

  5. I think your hunch is right. it doesn’t really matter how the system treats voters which don’t use all of the available votes or how support for parties is measured at the national level (which is what the ‘fictional voters’ mechanism is designed to check). However the party votes are determined, they are added up and allocated to parties using a simple proportional formula.

    Liked by 1 person

    • I agree. Or I think I do. I keep going back and forth on this.

      The problem is that if we are measuring effective number of vote-earning parties or disproportionality, it matters if the reported nationwide votes are weighted somehow. That is, I am not too worried about complexity here at the district level. But aggregations to national level may be suspect.

      I lean towards inclusion when in doubt. It is a big enough dataset that it won’t be too consequential for overall results, and if a given case stands out as anomalous, it can be explained.


      • I think you’d need to look at the particular weighting formulas for more clarity. But my understanding of them is that they’re meant to remove the problem that if you have (say) two seats in District X and fifty seats in District Y, the fifty votes from each voter in X don’t swamp the votes from District Y when you’re trying to work out national party strength. I would be more wary of using unweighted numbers of votes for this reason.


  6. Well, sometimes a peek at the data would have answered the question. Here is how the data are organized for one of the two constituencies in Liechtenstein for 2013:

    ctr_n yr cst mag pty pvs1 seat vv1 cv1 pv1
    Liechtenstein 2013 1 15 5 5.891520023 Missing Data 9375 Missing Data 55233
    Liechtenstein 2013 1 15 4 5.182506561 Missing Data 9375 Missing Data 48586
    Liechtenstein 2013 1 15 6 2.213119984 Missing Data 9375 Missing Data 20748
    Liechtenstein 2013 1 15 2 1.712853312 Missing Data 9375 Missing Data 16058

    ‘pvs1’ in the sixth column is party vote share (first/sole round). These are SHARES, so those numbers make no sense. The last column is party votes, which you might note are a lot higher than the column for “vv1” which is valid votes. Oh, and number of seats won are missing.

    Note that a total of 140,652 party votes are registered, by 9,375 voters. That is exactly 15 per voter. It seems unlikely that every voter used every one of the available votes, so these must be weighted some way.

    One could recalculate shares by re-weighting, For example, party (pty) 5 has 0.3928 of the vote; however, this is based on a fractional number of “votes” (because 55,233 divided by 15 is not a whole number). So I have no idea what it means. I will not use such data (even though I could probably get the seats data elsewhere).


    • Matthew,

      <> looks like it is <>/<> (total party votes over total valid voters), which certainly isn’t a ‘vote share’ as we use the term, but rather the mean number of votes cast per voter for that party.

      What is <>? The party id?

      This example from a single district with fewer than 10,000 voters in a principality with only two electoral districts suggests that it probably shouldn’t be classified as ‘simple’, right?


      • It looks like WordPress eliminated the letters inside my brackets. Oops.

        What I was trying to say is that it looks like ‘pvs1’ = ‘pv1’/’vv1’ (total party votes over total valid voters), which is the mean number of votes per voter for that party.

        And I was asking what ‘pty’ stood for.


      • Yes, those brackets will be interpreted as html tags!

        pvs1 is supposed to be party’s vote share in the district (in first round).

        pty is just a unique identifier for the party.

        (This is from CLEA.)


  7. I tried to post this here two days ago and have had some trouble…. What I had written was:

    I’m not contributing very much to the original conversation at this point, but I concur with Tom’s response re: how “simple” the free list can be.

    If the criteria for inclusion is “single-tier, single-round, party-vote system”, as Matthew says, then I would probably lean toward a ‘no’: any voter who casts fewer than M preference votes in a system where the preference votes used are not re-weighted to be equivalent to a single party-list vote–which is to say, most instances of this system–does not cast a ‘full’ party vote. (Moreover, whenever voters mix preferences across lists, the party-vote really becomes something like a functional equivalent of a party-vote, right?).

    Matthew, what do you mean when you say “it remains ‘simple’ in terms of how it processes the votes across lists”? Doesn’t this depend on the weighting mechanism the electoral authority adopts?

    There are obviously other complications. Some versions may be ‘simple’ (e.g. Luxembourg, where M is the same across the four districts and there is only a single tier), while others may not be (e.g. El Salvador and Honduras, where M deviates quite a bit; Ecuador, which used two tiers; Switzerland, which allows for the aforementioned multiparty alliances; or Liechtenstein, with only two districts but where it appears that voters may possess not only M individual votes but up to M party list votes).

    It’s amazing that there is so much variation in so few instances of this system!


    • Actually, in Luxembourg the district magnitudes of the four districts vary quite a lot, from 7 to 23. It is one of the reasons I like the case so much! Lots of M variation despite small S (assembly size).

      As for what I mean by the processing, I mean it takes a given vote share and turns it into seats via a PR allocation formula, within districts (I am not including any multi-tier systems for this particular analysis). See also the last sentence of hschlechta’s comment marked 30/12/2021, 2:27 am; I think that sums it up well. As far as I understand it, the only complexity involved is in that initial question, what is a “vote share” in a free-list system? (See also my response to hschlechta.)


  8. Pingback: The political system of Guyana | Fruits and Votes

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