The Myth of Perfect Proportionality
In European parliamentary democracies, the scene has repeated itself for decades: after elections, parties negotiate the formation of a government and divide up ministerial posts. It is a dynamic that, at least on paper, seemed to follow a simple, almost mathematical rule: the more seats you have, the more power you get. Yet what has long been considered a “law” of politics for over half a century may be far less solid than previously thought.
Calling into question one of the pillars of political science is a new study published in Political Analysis, titled “Refining Gamson: The Isometric Log-Ratio Transformation and Portfolio Proportionality in Multiparty Governments,” by Lanny Martin (Bocconi University) and Georg Vanberg (Duke University).
The conclusion is clear: the distribution of power in coalition governments is less proportional than commonly believed, more unstable and far more influenced by political context.
The “Law” That Wasn’t a Law
Since 1961, when American sociologist William Gamson formulated his theory, the so-called Gamson’s Law has dominated the study of coalitions: parties receive cabinet ministries in proportion to the seats they hold in parliament. This intuitive, almost self-evident idea has been confirmed over the years by dozens of empirical analyses.
But according to the authors, the problem lies precisely in how those analyses were conducted. “For years, we took for granted that the relationship was linear and stable,” explains Lanny Martin, Professor of Political Science at Bocconi University. “In reality, we were using statistical tools that are not suited to the type of data we are analyzing.”
The issue is technical but crucial: both seats and ministries are “shares,” parts of a whole that must always add up to 100%. This means they are not independent of one another, but interconnected. Ignoring this — as is often done — leads to distorted results.
A Methodological Error That Changes Everything
The study introduces a new approach based on the so-called ILR (isometric log-ratio) transformation, already used in other fields but never before applied to political science. Put simply, traditional models treat the data as if each party were independent. But in a coalition government, this is not the case: if one party gains a ministry, another must lose one. “It’s a zero-sum system,” Martin says. “If you don’t model it correctly, you end up seeing regularities that are actually statistical artifacts.”
The authors’ simulations show that traditional methods produce systematic errors: they overestimate proportionality and fail to capture differences across governments.
What Happens in Reality
Applying the new method to a large dataset — 910 parties in 308 governments across 16 parliamentary democracies — reveals a very different picture. The most striking result concerns proportionality: instead of the near “perfect” ratio estimated in the past, the relationship between seats and ministries is weaker. In practical terms, a 4% increase in seat share corresponds, on average, to only about a 3% increase in ministerial posts. And that’s not all. The presumed stability of the relationship disappears. “There is no universal rule that always holds,” Martin notes. “What we find is substantial variation: some governments are almost perfectly proportional, others much less so.” In numerical terms: of the 308 governments analyzed, 148 show significantly lower proportionality than traditional estimates, while only 17 appear more proportional.
The Hidden Advantage of Small Parties
One of the most interesting implications concerns smaller parties. In the past, scholars had already identified a “bonus” for small parties in coalition bargaining. The new study suggests that this effect is even stronger than previously thought. With weaker proportionality, smaller parties manage to secure more ministerial posts relative to their parliamentary weight, while larger parties face a relative penalty. “The system is not neutral,” Martin emphasizes. “It systematically favors those with fewer seats, especially in complex bargaining contexts.”
The End of a Certainty — and New Questions
The implications go beyond this specific case. If one of the most established regularities in political science turns out to be partly illusory, it raises the possibility that other findings may also depend on the tools used to obtain them. According to the authors, the proposed method can be applied to many other areas: from electoral competition to public spending allocation, and even media analysis. But above all, it changes how we interpret coalition politics. “Gamson wasn’t wrong,” Martin concludes. “But it’s not a law. It’s a tendency — and like all tendencies, it depends on context.”
In other words, behind the apparent mathematics of power, something far less predictable remains: politics.
