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Borda Count

Voting Systems

Borda Count

What is the Borda Count?

The Borda Count is a form of preferential voting where the rankings are converted into points, and the candidate who receives the most points is declared the winner.
The number of points per place is decided by the number of options on offer to the voter. Candidates score one point for being ranked last, two for being next-to-last and so on, with the first-choice candidate receiving points equal to the total number of candidates. So if there were seven candidates standing for election, a candidate receiving a first-preference vote would receive seven points.
Depending on where the method is used, the exact allocation of points varies. Some places, for example, give the last-choice candidate zero points. In Nauru, a candidate receives one point for a first preference, half a point for a second preference, one-third of a point for a third preference, and so on.

Real-world application of the Borda Count

  • Used for the election of two ethnic-minority members of the National Assembly of Slovenia.
  • The Parliament of Nauru.
  • Presidential elections in Kiribati.
  • Various private organisations and awards, such as the NBA's Most Valuable Player award and the Eurovision Song Contest.

Arguments used in support of the Borda Count

As well as the advantages it shares with other preferential voting systems such as the Alternative Vote and the Single Transferable Vote, the Borda Count tends to elect broadly acceptable candidates, rather than those supported by the majority. However, as it is possible for a candidate to have a majority of first preferences and fail to be elected, this is sometimes used as an argument against the Borda Count.

Arguments used against the Borda Count

There are two principal objections to the Borda Count.

Strategic nominations

Borda counts encourage a strategic approach by parties to nominations. An extra candidate increases the cardinal number of points in the system and alters the relativities between other candidates. A minority faction, by standing more candidates, can increase its chances of prevailing over a majority. For instance:
Suppose there are two broad factions in the group in which the election is taking place, one with 63 per cent support and one with 37. Suppose one candidate from the majority faction (A) and two candidates from the minority faction (B and C); say, further, that candidate B is widely respected while candidate C is not. This would give preference orders as follows:
A>B>C 63 voters (Borda points A 126, B 63, C 0)
B>C>A 37 voters (Borda points A 0, B 74, C 37)
Adding up the points, B wins with 127 Borda points, with A on 126 and C on 37.
There is an obvious response from the faction to which candidate A belongs – stand another candidate.
A>D>B>C 63 voters (Borda points A 189, B 63, C 0, D 126)
B>C>A>D 37 voters (Borda points A 37, B 111, C 74, D 0)
Thus, A now wins with 226 compared to 174 for B. The voters have not changed their minds at all from the earlier example.
However, if the B-C faction now stand more candidates, the advantage can flip back… Borda rules encourage a proliferation of more-or-less bogus candidates. Even if you do not have clear-cut factions, the examples clearly show that Borda counts can produce seriously distorted results that do not reflect the balance of opinion in the voting body, and are affected by arbitrary factors like the number of candidates in the field.

Tactical voting

Borda counts encourage tactical voting to an even greater extent than First Past the Post. Your expression of lower preferences can harm your first choice. In our first example above, if voters supporting the majority A faction ranked the other two candidates insincerely, putting C above B, they would successfully dish candidate B. In Borda there is always an incentive to give the strongest opposition challenger an insincerely low ranking. Suppose there is a Borda election in which Conservatives get 45 per cent, Liberal Democrats 40 per cent, and Labour 15 per cent of first preferences; and that voters vote ideologically (i.e. that Con voters prefer Lib Dem to Lab, Lab voters prefer Lib Dem to Con, and Lib Dem voters are evenly divided between the other two parties). The Borda result is:
45 voters choose C>LD>L (Borda points C 90, LD 45, L 0)
20 voters choose LD>C>L (Borda points C 20, LD 40, L 0)
20 voters choose LD>L>C (Borda points C 0, LD 40, L 20)
15 voters choose L>LD>C (Borda points C 0, LD 15, L30)
Borda outcome: C 110, LD 140, L 50)
So far so good – probably the outcome that any preferential system would produce. But if the Conservative voters really want to win, they should list Labour as their second preference regardless of what they actually believe. If they did this en masse, the Borda totals would be C 110, LD 95, L 95 – the Conservatives win.
Take it a step further – suppose that the Lib Dems, even those on the right who prefer the Tories to Labour – know that the Tories might well be voting tactically, and decide to do the same and dish their chances by refusing to give them any second preferences. The 20 LD>C>L voters then decide to cast their votes LD>L>C to do down the Tory. The result is that the Borda count is now C 90, LD 95, L 115 – and Labour win despite only having 15 per cent support.