Bigger Districts Don't Mean More Expensive Campaigns
One significant concern for many people about proportional and semi-proportional voting systems is that the cost of campaigning will likely rise with the increase in the size of the district and number of voters. As long as a legislative body maintains the same number of members, districts will need to be bigger with the use of a proportional voting system than with a one-seat district system because proportional systems require districts with at least three representatives.
Advocates of proportional systems argue that campaign costs are unlikely to go up -- or at least, each winning candidate will not need to spend more money to win and indeed will often require less. With a proportional system, the percentage of voter support necessary to win is less 50%; the winning threshold is 25% in a district with three representatives and 10% in a district with nine representatives. This lower threshold means that a candidate can focus on voters interested in electing them rather than on voters who don't much like them. In many elections, it is the last 10% of votes necessary for a candidate to gain over 50% that create the need for big spending. Indeed that is exactly what observers of politics in Illinois have said about the impact on campaign finance of replacing cumulative voting (where it took 25% to win a seat) with one-seat districts in 1980 for elections to the state house of representatives.
Now it turns out that even winner-take-all elections in multi-seat districts need not be more expensive for candidates.
More states need to be analyzed, but the findings are quite surprising in the two for which we have data: North
Carolina and Vermont, both of which have a mix of one-seat districts and multi-seat districts. In these states, candidates
actually spend less in the bigger, multi-seat district elections than in the one-seat districts. The reason for this
apparent paradox probably is twofold: candidates from one party can pool some of their expenses (activities designed
to get out the vote, mailings, some advertisements) and it may be harder to pursue negative campaigning when
there are several viable candidates on the ballot.
North Carolina Analysis
This data shows that North Carolinian General Assembly candidates typically spend less in multi-member districts than in single-member districts.
The figures are for 1996, but the basic pattern holds for other elections in the 1990s, which is the period we have this data for. (The VT figures are pretty incredible... $1,400 for a seat in the state House... what a bargain).
The chart below (credit to Democracy South) is based on the expenditures in the 1996 cycle for the general election for contested races among major party candidates. It excludes funds spent in a contested primary (expenditures through 30 days after the primary for primary contestants) and excludes funds spent as donations to other candidates or to state or national parties (since these funds aren't really used for the candidate's election; this eliminates the leadership money raised and then sent to other candidates or party committees). It only includes democrats and republicans; hardly any minor party or independent candidate spent beyond the $1000 reporting threshold. It also excludes the districts where the major party candidate(s) only faced a minor party candidate in the general election.
Note that North Carolina has multi-member districts for the Senate (all 2 seaters) as well as the House (some 2 seat, a few 3 seat district). All together there are 25 multi-member districts (23 had contested races among major party candidates in 1996) and 115 single-member districts (68 had contested races among major party candidates in 1996)
Expenditures for the 1996 General Election by Democratic and Republican Candidates in Contested Races for the North Carolina General Assembly:
We also have data on campaign costs in Vermont's 1996 elections.