A Formal Model of Learning and Policy Diffusion

This is a review of A Formal Model of Learning and Policy Diffusion (2008) by Craig Volden, Michael M. Ting, and Daniel P. Carpenter. American Political Science Review 102 (August): 319-332. You can find the original in Google Scholar.

Much of the empirical work to date has not adequately distinguished [game-theoretic] learning-based policy diffusion from [decision-theoretic] myopic individual adoptions.

Those who advocate federalism argue that devolution improves policy outcomes nationwide by providing opportunities for local experimentation. In the words of Louis Brandeis, justice of the U.S. Supreme Court (1932):

It is one of the happy incidents of the federal system that a single courageous state may, if its citizens choose, serve as a laboratory; and try novel social and economic experiments without risk to the rest of the country.

These claims have inspired a literature on “diffusion,” mostly focused on the American states, that has asked whether there is evidence that the states do, in fact, learn from one another. For the most part, the existing literature has concluded that diffusion occurs regularly among the American states, although there is some disagreement as to the mechanism.1

By contrast, Volden, Ting, and Carpenter argue that none of the existing work (including their own previous work on diffusion, apparently) has provided any evidence of policy diffusion. The methods and assumptions used in previous research cannot differentiate between innovation (isolated experimentation by myopic states) and diffusion (learning from experiments in other states).

Overview of the Model

To correct this problem, the authors present two formal models of experimentation. Both begin from the same basic setup: States have policy makers (legislators, bureaucrats, whatever) that can be placed along a unidimensional ideological line (i.e. we can classify the state as conservative or liberal). Within a particular issue area, there is a status quo policy and a proposed experimental policy. Each policy has two characteristics. First, it can be placed along the ideological line, and this “spatial” characteristic is common knowledge–that is, everybody agrees as to which policy’s goals are more liberal or conservative. Second, each policy has a “valence”–that is, each policy might be more or less effective at reaching its stated goals.

Although each proposal’s “spatial” characteristics are assumed to be common knowledge, “valence” is known only for the status quo–the experimental proposal’s valence is unknown. Thus, policy makers have a choice: They can stick with the status quo (with known valence) or they can switch to the experimental policy (with unknown valence). If they choose to experiment, then in “period two” (e.g. the next legislative session), when the experimental policy’s valence is known, they can choose to stay with the new policy or revert to the old one.

After setting up this basic model, the authors derive two models from it. The first is a decision-theoretic model that assumes each state exists in isolation; states may innovate similar policies, but there cannot (by definition) be diffusion. The second is a game-theoretic model that assumes each state can learn from policy experiments in other states; either innovation or diffusion can occur.

The decision-theoretic model

In this model, states do not have the option of learning from other states’ experiments.

In an extremely liberal state, the policy makers will choose the most liberal policy proposal, regardless of expectations about valence. (Likewise for extremely conservative states). But in moderate states, policy makers will balance valence against ideology. A moderate conservative would prefer an efficient but liberal policy over an inefficient but conservative policy; a moderate liberal would prefer an efficient but conservative policy over an inefficient but liberal policy. These are the conditions under which innovation occurs.

Thus, we would expect to see only moderate states experimenting. If they learn that the policy is inefficient, then they would revert to the previous policy–the one that is ideological preferable.

The game-theoretic model

In this model, states do have the option of learning from other states’ experiments.

If states can learn about a proposed policy’s valence by observing policy experiments in other states, then the incentive to experiment drops. Experimentation is risky; if you can learn from others’ mistakes rather than having to make those mistakes yourself, then why experiment at all? As such, those policy makers willing to experiment will fit into a narrower ideological range than those willing to experiment in the decision-theoretic model.

Implications for the Literature

Previous work on “diffusion” has not appreciated the differences between these two models. All of the evidence for policy diffusion presented in previous work can be explained in terms of the decision-theoretic model. In order to conclude that diffusion actually occurs, we must find evidence of behaviors that are predicted by the game-theoretic model and NOT by the decision-theoretic model.

The literature has presented five different causal mechanisms to explain “diffusion,” but all five mechanisms can be explained with the decision-theoretic model:

  • Walker says some states are inherently more disposed to innovate than others.
  • Gray says diffusion happens when states face similar policy problems.
  • Others say that diffusion happens when neighboring states are ideologically similar.
  • Still others say that diffusion happens when any states (neighboring or not) are ideologically similar.
  • A final argument is that diffusion happens when policy advocates take their arguments to multiple states.

As the authors put it: “Much of the empirical work to date has not adequately distinguished [game-theoretic] learning-based policy diffusion from [decision-theoretic] myopic individual adoptions.”

The authors conclude by listing specific empirical implications of their model that future research should evaluate in order to determine whether or not diffusion actually occurs.


Much of the work on diffusion was published in the 1960s and 1970s. I suspect that modern political scientists have hesitated to take up the question again because they thought it was settled. This article demonstrates persuasively that the question is far from settled. This is the article’s most important contribution–to point out that we do not yet have any evidence that states do (or do not) act as “laboratories of democracy” that learn from one another. This question is normatively important; if states do not learn from one another, then we lose an argument for devolution.

However, I was less than satisfied with the authors’ empirical suggestions. They conclude by pointing out several ways that we can use their theory to empirically determine whether states follow the decision- or game-theoretic model. Unfortunately, these empirical implications are extremely nuanced and may be difficult (or nearly impossible) to apply in practice.

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  1. Mariely Lopez-Santan Unregistered
    Posted March 3, 2009 at 11:43 am | Permalink

    A brief comment… I do not think the issue of innovation and diffusion was settled in 1960s and 1970s. I believe it has to do with the difficulties of capturing, measuring and gathering data on this issue. Nonetheless, in comparative politics this type of work is still very much relevant. For instance, one must look at the literature on social policy diffusion, on the OMC in the European Union (for instance) and these issues of learning are all over the place.

  2. Posted March 4, 2009 at 12:10 pm | Permalink

    I tend to agree that it was not settled in the 1960s and 1970s–although within the U.S. state politics literature, there was a flurry of activity during that time, followed by a long stretch of only sporadic attention to the question. I can’t speak for the EU lit, though, so thanks for the note.