"Wasted" Votes and "Excess" Votes on the Last Count

The matter of "wasted votes" is a recurrent theme in discussions of electoral systems, particularly in first-past-the-post systems like those of the United States and the United Kingdom. When a candidate with 49% of the vote fails to gain the seat that is won by the candidate with 51% of the vote, then the voters who supported the losing candidate are seen as having cast "wasted" votes.

The single transferable vote (STV) system holds out the promise of avoiding such spectacular "waste" by creating multi-member constituencies and by allowing votes to be transferred from candidates who have no further need of them, to other candidates that may utilize them.

Yet the question of "wasted votes" is also an issue in STV countries like Malta. The problem here arises from the use of the so-called Droop Quota. This formula defines the quota required for election as the number of votes cast divided by the number of seats to be filled, plus one. Thus, if 10,000 valid votes are cast and five seats are to be awarded, then the number of votes required for election is not 2,000 (i.e., 10,000 divided by five) but rather 10,000 divided by 5+1, or 1,667 votes.

An inevitable consequence of the Droop Quota is that, when all candidates in a constituency have been declared elected, there will remain some other candidate(s) with accumulated votes who will not be elected and whose votes cannot be transferred. These unused votes on the last count -- totaling the size of a single quota -- are then, in a sense, wasted.

This phenomenon raises both theoretical and practical questions that will be addressed in a future note on this Web site. In the meantime, here are some tables from actual Maltese experience that may be of use in illustrating this aspect of STV.

The first table shows the candidates with unused votes on the last count. These involve the "wasted" votes [PDF] that figure so prominently in discussions of STV in Malta.

The following two tables are on related aspects, both resulting from situations when no further vote transfers would affect the outcome.

A listing of candidates who, on the last count, still had votes in excess of the quota [PDF] yet where these extra votes could not be transferred to another candidate.

And the candidates who were elected without reaching the quota [PDF] on the last count.