US Presidential elections are indirect: the people vote for an electoral college and the electoral college votes for the President. States assign electors in a winner-takes-all manner (either state-wide or per district), which leads to the campaign being focused on swing states. In United Kingdom parliamentary elections, each constituency elects one MP in a first-past-the-post system. Many constituencies are virtually certain to remain with a particular party (safe seats).
In both cases, I could imagine that someone living in a safe state or safe seat may be less motivated to vote, than someone living in a swing state or marginal seat. Is there any evidence that turnout is higher in swing states than in safe states, and/or higher in marginal seats than in safe seats?
Competiveness and the feeling (justified by recent history) that your side has a decent chance to win, increase turnout; this fact is supported by all 7 of the following studies:
(note: some of these pertain to FPTP elections but possibly not all). Caveat: I personally didn't check the validity of RangeVoting's conclusion that all 7 studies support this.
G.Pillsbury, J.Johannesen, J.Arp: America Goes to the Polls A report of voter turnout in the 2006 election, www.nonprofitvote.org. (On page 9: the "non-competitive" states had 37% turnout and the ones with "competitive" governor and/or senate races had 45%.)
Vanderleeuw JM, Liu BD: Political empowerment, mobilization, and black voter roll-off, URBAN AFFAIRS REVIEW 37,3 (Jan 2002) 380-396
Endersby JW, Galatas SE, Rackaway CB: Closeness counts in Canada: Voter participation in the 1993 and 1997 federal elections, JOURNAL OF POLITICS 64,2 (May 2002) 610-631
Nicholson SP, Miller RA: Prior beliefs and voter turnout in the 1986 and 1988 congressional elections, POLITICAL RESEARCH QUARTERLY 50,1 (Mar 1997) 199-213
HILL KQ, LEIGHLEY JE: PARTY IDEOLOGY, ORGANIZATION, AND COMPETITIVENESS AS MOBILIZING FORCES IN GUBERNATORIAL ELECTIONS, AMERICAN JOURNAL OF POLITICAL SCIENCE 37,4 (Nov 1993) 1158-1178
SE Galatas: Electing the first parliament – Party competition and voter participation in Scotland, PARTY POLITICS 10,2 (Mar 2004) 213-233
Christine Fauvelle-Aymar & Abel Francois: The impact of closeness on turnout: An empirical relation based on a study of a two-round ballot, PUBLIC CHOICE 127, 3-4 (Jun 2006) 469-491
Abstract: Several methodological difficulties emerge from the empirical evaluation of the impact of closeness on turnout. The most critical resides in the use of the actual electoral results to assess the impact of closeness. Important doubt therefore remains with respect to the empirical validity of the relationship between turnout and closeness. This article intends to explore this ambiguity by an econometric analysis of the two-round French legislative elections. The first ballot gives excellent information to the voters on the expected closeness of the upcoming second ballot. The results show that closeness, whatever its measure, has an important and meaningful impact on electoral participation.
However, there are studies (including reviews) supporting opposite view:
Some evidence also points to voters themselves being quite different in competitive environments than uncompetitive ones. Voters in closely contested elections accumulate more information about the candidates and the race (Gimpelet al., 2007; Hill and McKee, 2005)
Whether voters in competitive environments act in similar ways to voters in uncompetitive ones is, however, a wide open question. Apart from the “minimal effects” presumption of yore that campaigns do not have meaningful influences (for a review, see Brady et al., 2006), more recent work by Holbrook and McClurg (2005) and Gerber et al. (2009) suggests that competition and state-level disparities in campaign attention have very limited impact on voter turnout.
It has been suggested that one of the reasons why majoritarian electoral systems are associated with lower voter turnout in comparison to proportional electoral systems is that citizens in uncompetitive districts ("safe seats") are not motivated to vote. ... I argue that, due to this difference, the impact of district-level competitiveness on turnout is stronger in mixed-member majoritarian (MMM) than in Mixed-member proportional (MMP). An analysis of district-level electoral data from four countries confirms this hypothesis.