Low levels of citizen participation in politics have long been seen as a serious democratic problem, and a possible relationship between turnout and election outcomes is a prominent topic of discussion in political science. The most frequent claim is that left-of-centre parties benefit from higher levels of turnout since many of them are disproportionately supported by groups on the lower end of the socioeconomic scale, such as the unemployed or low wage earners.

In a recent study, we showed that Norway is one country in which changes in turnout are likely to be a mixed blessing for the left. In Norway, the anti-immigration Progress party on the right competes with Labour for support from those in lower socioeconomic groups, while the voter profile of the Socialist Left fits the "new left" label. Thus, we would expect that a sudden shift in voter turnout due to more voters from lower socioeconomic groups showing up at the polls would benefit the Labour party and the Progress party, while the Socialist Left party would suffer.

In two-party systems, this relationship between turnout and election outcomes has received some empirical support, yet the evidence is not conclusive. In multiparty systems, the evidence is less clear and a potential relationship is likely to depend on the specifics of the party system and party competition in each country. In particular, most western European countries have witnessed the establishment and subsequent growth of new left and new right parties. Electoral support for new left parties does not come primarily from the lower socioeconomic groups that have been the main constituency of traditional social-democratic parties. By contrast, support for hard right parties often does. Thus, to the degree that increases in turnout imply that more people from lower socioeconomic groups are voting, we would expect some left-of-centre parties to benefit, while others would suffer, and similarly on the right.

The key empirical challenge in this type of research is to isolate the effect of turnout from the myriad other factors that operate in an election. In order to do so, we study the introduction and removal of a reform of early voting, which made it possible to vote early at the local post office. The reform reduced the costs of voting and led to a massive increase in early voting. In fact, survey data estimates suggest that the reform increased total turnout by about two percentage points.

The reduction in the costs of voting was larger in rural areas, and in line with this we found that increases in turnout were larger in rural areas. Moreover, we found that individuals with lower levels of education were mobilised by the reform, in particular in rural areas. The characteristics and the geographical impact of the reform allows for a research design where we examine the trends in turnout and election outcomes before and after the reform, and how the trends depend on the type of municipality. Since the reform affected turnout more in rural areas, but had little impact in urban population centres, we can use this variation to estimate the impact of turnout on party vote shares.

The empirical results are consistent with several of our expectations. In particular, the trends in the vote share of the Labour party and the Progress party were significantly stronger in areas where turnout increased. Compared with the average municipality, Labour's vote share decreased by about 0.8 percentage points more in municipalities where turnout did not increase, compared to the most rural municipalities. The Progress party's vote share trend was negative, yet this trend was a lot more pronounced in urban municipalities where there were no positive effects of the reform on turnout.

Similarly, our results for the Socialist Left party are also as expected. They deviated negatively from the municipal trend in those areas where the reform had the most impact on turnout. In particular, their vote share increased about 0.4 percentage points more in urban areas with no increase in turnout, compared with the most rural areas. When we use the reform-induced geographical variation in turnout to estimate the effect of turnout, we find that a one percentage point increase in turnout causes the vote share of Labour to rise by an estimated 0.9 percentage points. The corresponding figure for the Progress party is about 0.8 percentage points. The Socialist Left and the Conservative parties, on the other hand, suffer if turnout increases.

How open to generalisation are our results? Since our research strategy builds on the geographical variation in our estimates, they are directly informative about the effects of changes in turnout on election outcomes in rural areas. Translation to urban areas depends on how different the rural and urban non-voters are. The reform led to a broad decrease in the cost of voting and in this sense it is similar to other reforms that alter the costs or benefits for a broad segment of the population, such as motor voter programmes or compulsory voting.

What about external validity beyond the Norwegian context? The Norwegian case is similar to most other western democracies in that voter turnout is biased against the participation of lower socioeconomic groups. It is also similar to other western multiparty democracies in that there exists a new right party as well as a new left party. Indeed, we find suggestive evidence from the most recent parliamentary elections in western European countries are consistent with some of the patterns we find in the Norwegian case: new right parties do better in elections with a high level of turnout, while new left parties do worse.

• This blog originally appeared on LSE's EUROPP blog