The authors look at the US Congress and uncover a hump-shaped relationship between the number of votes an interest group's members represent and monetary donations by the group to the politician. In other words, it turns out that the most populous groups need not donate much to get a politician to do their bidding. More specialised concerns, on the other hand, have to make up for the shortfall in numbers with hard cash (which is in turn used to 'impress' susceptible voters):
The role played by special interest groups in shaping policy-making is hard to ignore. One simple reason is the considerable size of the amounts the special interest groups (SIGs) inject into the political system.
[...] since the probability of being (re-)elected ultimately depends on the number of votes a politician can attract, the legislator should take into account both the electoral strength of an interest group (i.e. the share of voting population it represents) and its contributing possibilities when deciding whether to support or not legislation in favor of such group.
The main contribution of the paper is to show that the number of voters represented by interest groups is an important variable in explaining the pattern of campaign contributions. The data indicate that an inverted-U shape describes the relationship between the share of voters represented by an interest group and the contributions to a legislator.
[...] we find that an additional vote costs a politician between 100 and 400 dollars depending on the district.
The theory is elegant (and convincing), and the empirics plausible. Advice to voters: with the dollar at record lows, datacharmer recommends you take the cash deal.
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