>it reveals that empirically, it produces a narrower political dialogue, poor participation, and low satisfaction with government compared to systems that produce better proportionality.

I am very skeptical of studies purporting to run statistical analysis on such small data sets as the recent history of countries, let alone the recent history of democracies. It seems that in the quest to produce quantitative political science research, people forgot all the statistical lessons about sample size, confounding factors, and so forth.

Weak empirical data is still stronger than abstract speculation with no evidence.

That's not true. The conclusions you derive from the data can be totally wrong because of how weak the data is, but now you have a false confidence in it.

First, that's at least as much of a danger with basing conclusions on abstract speculation without evidence, and second, that's not a matter of which is stronger, it's a matter of treating either as stronger support than it is.

For us who haven't seen Lijphart's _Patterns of Democracy_, how does one establish such a conclusion, measure the width of political dialogue, for that matter? It would seem that a proper, randomised trial could be difficult to make, or has it been done on a small scale and extrapolated to country size?

One measure could be the typical voter turnout in elections. Lower turnout could mean less trust in the political system.

    United States (2016): 56%
    India (2014):         65%
    Germany (2017):       76%
    Denmark (2015):       86%

Voter turnout essentially reflects whether their vote is worth it. If they think everything is going to get worse no matter how they vote, they won't bother. But the same happens when they think everything will be alright no matter how they vote! So you can't really distinguish between those cases based on voter turnout alone.

The short version is you compare actual existing democracies on multiple axes.

The long version is, well, Lijphart's Patterns of Democracy.