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.

Critique

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.

Theories

Proximity theory is the best-known of these three theories. It makes a basic claim: If you line up all the candidates from most liberal to most conservative, voters will pick the candidate whose ideology is most similar to their own. This theory serves as a basic assumption of the median voter theorem and other spatial models.

Discounting theory is similar to proximity voting, but with a recognition that winning candidates will have to battle other elected officials to get anything done. Imagine a genuinely moderate voter who desires middle-of-the-road policies. If the president is a staunch conservative, then that voter might prefer an extremely liberal Congress over a moderate Congress, given that actual policy outcomes will lie somewhere between what Congress and the president wants. Thus, a discounting voter weights candidate proximity based on the status quo.

The third theory, directional theory, argues that voters view the world in black and white. They want to vote for whichever candidate is on their side of the issues. For example, a moderate Republican would rather vote for an extremely conservative Republican than for a moderate Democrat, because the Republican is on the same side of the issues as the voter is–even if the moderate Democrat is closer to the voter ideologically.

Test

Previous attempts to test these three theories against one another empirically have run into several problems. For one thing, candidate positioning is endogenous–candidates try to place themselves ideologically in a winning position. There have also been a variety of measurement problems.

The main problem, though, has been a lack of critical tests. Previous research has not spelled out the exact circumstances under which these three theories yield different empirical results. The authors begin by filling that gap with a formal model. They show that only for voters within a narrow ideological range do the proximity and discounting rules produce divergent predictions; likewise, the proximity and directional rules produce divergent predictions only within another narrow ideological range. (See Figure 1, Table 1, and Figure 2 in the article for summaries of these scenarios.)

Knowledge of these ranges enables the authors to design critical tests of the theories with a simple experimental survey. Three survey questions provide most of the necessary data. First, they ask voters to place themselves on an 11-point ideological scale dealing with health care reform. Second, they ask them to choose one of two hypothetical candidates based only on each candidate’s position on this 11-point scale. And third, they ask voters to place current government policy along this 11-point scale.

Results

Using sophisticated statistical analysis of these data, the authors find that proximity voting is by far most common, followed by discounting and (distantly) directional voting. There is considerable heterogeneity within the sample; 57.7% are proximity voters, 27.6% are discounters, and only 14.7% are directional voters.

Demographic factors help explain some of this heterogeneity. For example, directional voter was twice as common among less educated respondents as among more educated ones. Most interestingly, discounting was much more common among moderates and independents,¹ a finding that may help explain why candidates polarize rather than converging to the ideological center.²

Critique

The authors provide a rigorous answer to a long-unanswered question. Their formal model is thoroughly persuasive, and it shows exactly where the three theories diverge. Thanks in large measure to this formal model, the authors have a compelling paper.

The empirical work is interesting, but I question whether they have underestimated discounting (and overestimated proximity voting). They do acknowledge a potential bias in this direction (p 310), but only in passing. My concern: When voters choose a hypothetical candidate in step two of the questionnaire, how do we know they are not taking account of the status quo? If they are, then they are making a discounted decision–not a proximity decision.

The authors attempt to control for this through question ordering–that is, by placing the status quo question last, not first, so as not to prime respondents toward discounting. But even if the status quo question were absent altogether, you still might have respondents considering the status quo when choosing a candidate. After all, when voters show up on election day, there is not a question on the ballot asking them to place status quo policies on an ideological scale–yet it appears that at least 27.6% of voters do so.

This article did set up a critical test between directional voting and the other two theories, but it did not set up a critical test between proximity and discounting. Granted, it showed that discounting is more common among moderate/independent voters than among others, but that’s only a marginal effect–a worthwhile finding, but not an answer to the puzzle.

Punchline: A significant contribution to this literature, but not a final answer.