Disclaimer. Don't rely on these old notes in lieu of reading the literature, but they can jog your memory. As a grad student long ago, my peers and I collaborated to write and exchange summaries of political science research. I posted them to a wiki-style website. "Wikisum" is now dead but archived here. I cannot vouch for these notes' accuracy, nor can I say who wrote them.
Stokes. 2005. Perverse accountability: A formal model of machine politics with evidence from Argentina. APSR 99: 315-26.
"Political machines (or clientelist parties) mobilize electoral support by trading particularistic benefits to voters in exchange for their votes. But if the secret ballot hides voters' actions from the machine, voters are able to renege, accepting benefits and then voting as they choose. To explain how machine politics works, I observe that machines use their deep insertion into voters' social networks to try to circumvent the secret ballot and infer individuals' votes. When parties influence how people vote by threatening to punish them for voting for another party, I call this perverse accountability. I analyze the strategic interaction between machines and voters as an iterated prisoners' dilemma game with one-sided uncertainty. The game generates hypotheses about the impact of the machine's capacity to monitor voters, and of voters' incomes and ideological stances, on the effectiveness of machine politics. I test these hypotheses with data from Argentina."
First, how does the machine know whether you followed through on your commitment to vote for it? Second (assuming the machine can monitor voting), what kinds of voters do machines target?
Dixit and Londregan (1996) and Cox and McCubbins (1986) are useful, but neither deals adequately with the commitment problems; in particular, they don't deal with the parties' ability to monitor a pork recipient's commitment to vote for you. (They also assume away that the parties will actually carry out their promises, but Stokes seems to do something similar.)
Because these models are one-shot games, this commitment problem undermines the models. At root, there is a prisoner's dilemma between the voter and the party (see Table 2, p 320), and it takes a dynamic (repeated) game to explain how cooperation can emerge.
First, machines can monitor votes. Though Stokes admits that this monitoring may be imperfect, she presents evidence that even in places with a (technically) secret ballot--like Argentina--parties seem to know how people voted, especially in rural areas.
Second, machines can detect voter types (i.e. each voter's ideological preference between the two parties). Again, this is particularly easy in small communities.
Also, this is a two-party model. Stokes does not consider whether a multiparty model would look different.
Critically, both sides must see their interaction as continuing indefinitely into the future. Thus, the machine retains some ability to distribute pork even when it finds itself in opposition (perhaps by using public funds, perhaps by getting donations from private actors that expect policy favors later on).
See Figures 1 and 2 (pages 319-320). Voters to the left of the median voter (X*) favor the machine party (party X1); voters to the right of the median are opposed to the machine. But depending on the size of the benefits (b) that X1 is willing to give in exchange for votes, there is a group of voters to the right of the median that is only "weakly opposed" to the machine. This group of weakly opposed voters is bounded by the median (who is indifferent) on the left and the point defined by equation 2 (p 320) on the right. And equation 2 reflects two variables: First, the probability that the machine can catch voters that accept benefits but don't vote for the machine, and second, the discount rate of receiving future benefits from the machine (i.e. how much the voter cares if the machine catches him defecting). (The party plays a "grim trigger" strategy; thus, if it catches a voter "defecting" (accepting goods but not voting for the machine) even once, then that voter loses the opportunity to ever again receive goods.)
Loyal voters cannot extract goods from the machine; to do so, they would have to threaten to support the opposition party if the machine fails to give them goods, but this threat would not be credible.
Stokes presents evidence from Argentina supporting the model's predictions:
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