Quota Borda system

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The Quota Borda System QBS is a PR electoral system for use in multi-member constituencies.  Imagine a six-seater constituency in a plural society of three dominant groups, where the three groups are roughly 30:30:30.  (There were many such constituencies in pre-war Bosnia.)  Success in a QBS depends on a good number of top preferences and/or a good Modified Borda Count MBC score; see below.

Lest their members/supporters split the vote, the matrix vote – like RCV (PR-STV) – prompts all parties to nominate only as many candidates as they think might get elected.  At the same time, the MBC element of a QBS encourages the voters to submit a full ballot.  Accordingly, in a 6-seater 30:30:30 constituency (in Bosnia), each faction could expect to win 2 seats; at the same time, those parties which do not fall into one of the country’s three ethno-religious categories (like Bosnia’s Social Democrats) might also hope for some success.

Now in many countries, not least those democracies which make decisions in binary votes, societies tend to divide into two: left- or right-wing, socialist or capitalist, and so on.  Likewise, in many societies already divided, each ethno-religious grouping tends itself to divide into two, to have a more radical and a more moderate party; (this was true both in Northern Ireland and in Bosnia).  Accordingly, in a 30:30:30 constituency, each of the two main parties in each ethno-religious grouping, might like to nominate 2 candidates; but no grouping would want to nominate more than 4.   Meanwhile, others like the Social Democrats might also have a good chance.  So that’s 14 candidates already, but not too many more.

Come the vote, every voter would be encouraged, by the MBC element, to cast a full ballot of 6 preferences.  In this way, QBS entices voters to cross the gender gap, the religious divide and even the sectarian chasm; the methodology is ideally suited to plural societies, and especially conflict zones.

In a six-seater constituency, the analysis proceeds as follows, counting:

(a)        all the candidates’ 1st preferences;

(b)       all the candidate pairs’[1] 1st and 2nd preferences; and

(c)        all their MBC scores.

At each stage, if there are still candidates to be elected, the count proceeds to the next stage.  In the analysis:

Part I


(i)        all candidates with a quota of 1st preferences are deemed elected;

          (ii)        all pairs of candidates with two quotas of 1st/2nd preferences are elected;

then, in

Part II, in which any candidates elected in Part I, in stages (i) or (ii), are no longer counted,

          (iii)       candidates with the highest MBC scores are elected.

QBS has only one count, albeit of three different types of totals: (a), (b) and (c); next, in the analysis, three different stages.


Dummett, M               1984, Voting Procedures, Oxford University Press, Oxford.

Emerson, P                  2016, From Majority Rule to Inclusive Politics, Springer, Heidelberg.

[1]                Consider, for example, the situation (which existed in Northern Ireland) where a father stood alongside his son.  If x people vote 1st/2nd dad/son, while y people vote 1st/2nd son/dad, and if x + y > 2 quotas, then this dad/son pair is said to have two quotas.