Under the approval voting system, the ballot paper would look similar to a FPTP ballot paper, and candidates would vote by marking X on the paper. However, unlike FPTP, candidates may vote for as many candidates as they like - that is, for all the candidates of whom they "approve". In each constituency, votes are counted and the candidate with most votes wins.
Approval voting is in use in several local legislatures in the United States, and its advocates note that it has several advantages over FPTP, with more moderate candidates with wider appeal tending to win.
The Wikipedia article on approval voting provides further details and notes that modifications are available, so for example approval voting could be used in the context of a two-round vote, or that preliminary eliminations could be incorporated.
However, LCER does not believe that approval voting should be a first choice for a system to replace FPTP in the UK. Because voting is on the basis of single constituencies, there is no guarantee that approval voting would yield a proportional outcome in aggregate terms in a general election. This is the same critique that may be made of the alternative vote (AV) - although AV is a good system for electing a single individual, such as a mayor or a party leader, to office, it is not a good system for electing a whole parliament.
Additionally, where a single individual is being elected, we tend to prefer AV over approval voting - AV allows voters to express a clear first choice and to rank their choices, and also makes clear that however many candidates a person votes for, only one of their votes "counts" at a time.
Approval voting may also be more subject to tactical voting. For example, suppose two voters think A is a great candidate and B is just marginally better than C, D, E F and G. If everyone else's votes would result in B winning the final place, just one vote ahead of A, then expressing preferences for both A and B would leave B ahead. To get their favourite candidate ahead the two voters need to vote for A and express no other preferences so that the two extra votes put A ahead.
