Social Choice and Welfare

, Volume 40, Issue 2, pp 353–358 | Cite as

The original Borda count and partial voting

  • Peter EmersonEmail author


In a Borda count, bc, M. de Borda suggested the last preference cast should receive 1 point, the voter’s penultimate ranking should get 2 points, and so on. Today, however, points are often awarded to (first, second,..., last) preferences cast as per (n, n−1, ..., 1) or more frequently, (n −1, n−2,..., 0). If partial voting is allowed, and if a first preference is to be given n or n − 1 points regardless of how many preferences the voter casts, he/she will be incentivised to rank only one option/candidate. If everyone acts in this way, the bc metamorphoses into a plurality vote... which de Borda criticized at length. If all the voters submit full ballots, the outcome—social choice or ranking—will be the same under any of the above three counting procedures. In the event of one or more persons submitting a partial vote, however, outcomes may vary considerably. This preliminary paper suggests research should consider partial voting. The author examines the consequences of the various rules so far advocated and then purports that M. de Borda, in using his formula, was perhaps more astute than the science has hitherto recognised.


Social Choice Approval Vote Counting Procedure Borda Count Plurality Vote 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


av (= irv = stv)

alternative vote

irv (= av = stv)

instant run-off voting


proportional representation

stv (= av = irv)

single transferable vote


Borda count


modified bc


quota Borda system


two-round voting


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Arrow KJ (1963) Social choice and individual values. Yale University Press, New Haven and LondonGoogle Scholar
  2. Black D (1958) The theory of committees and elections. Cambridge University Press, CambridgeGoogle Scholar
  3. de Borda JC (1781) Mémoire sur les élections au scrutin, Mémoire de l’Académie Royale. Histoire de l’Académie des Sciences, Paris, pp 657–665Google Scholar
  4. Dummett M (1997) Principles of electoral reform. Oxford University Press, Oxford, pp 150–151Google Scholar
  5. Emerson PJ (1994) The politics of consensus. Samizdat, BelfastGoogle Scholar
  6. Emerson PJ (2007) Designing an all-inclusive democracy. Springer, Heidelberg and BerlinCrossRefGoogle Scholar
  7. McLean I, Urken AB (1995) Classics of social choice. The University of Michigan Press, Ann ArborGoogle Scholar
  8. Saari DG (2001) Decisions and elections, explaining the unexpected. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  9. Saari DG (2008) Disposing dictators, demystifying voting paradoxes. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  10. Sigmund PE (1963) Nicholas of cusa and medieval political thought. Harvard University Press, CambridgeGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.The de Borda InstituteBelfastNorthern Ireland, UK

Personalised recommendations