Perhaps a compromise or judicious position would be that anyone interested in democracy should pay attention to both left and conservative parties, though political sociologists often would rather study the left (myself included).
Mudge’s book is impressive in its scope with regards to years of history (about 1890 to 2005) and the number of countries she considers in narrative detail. The natural inclination for most sociologists would be to go straight to the major politicians and see what influenced them. Instead she focuses on the party theoreticians and major economists, which are the Ministers of Finance (Sweden and Germany), the Chancellor of the Exchequer (UK), or Secretary of Treasury (US). She examines left party political platforms and this involves considerable translational efforts. She constructs a neoliberalism index for the center left and the center right, but only maps out the US figures for this. Otherwise, the scores are aggregated for bundles of countries in regime types. Her conclusions that party theoreticians abstained from intervention (circa 1920), party Keynesian economists fully embraced government intervention (circa 1960 but beginning in the 1930s), and transnational finance-oriented economists deregulated (circa 1995) is conclusively shown for the United Kingdom and Sweden.
For the US and Germany her thesis can be generally accepted as a tendency, but it is less persuasive in terms of a full explanation. For the US, the first period is the problem. She decides not to cover it because there was no left party. However, this ignores the influence of Henry George’s Progress and Poverty, the progressive movement, the governmental reining in of the robber barons with anti-trust, and the impact of Woodrow Wilson’s two Secretaries of the Treasury, one who averted a financial run at the beginning of World War II withdrawing all their money from the US economy to fight a war by closing the NY Stock Exchange, and the other by establishing the Federal Reserve – both notable economic interventions. That they are not labor or social democratic parties is correct, but that statement applies equally well to the whole history of the Democratic Party. Also, one might want to tip their hat to Eugene Debs running for president. Germany might be less of a problem, but one has to note that having been Nazified in 1933, Germany no longer fits her thesis since Hitler banned and then persecuted left parties.
The neoliberal period (centering on 1995) also has a problem with Germany. It would have been helpful if Mudge had used the Millsian method of difference or even better concomitant variation rather than the method of agreement. The method of agreement largely assumes that all the countries are the same in neoliberalism. As only the US positive scores are reported, it is hard to know what the other three countries are on the scale. I would expect all left parties to become more neoliberal (as per her combined regime scores show), but I would contend that Germany is the least neoliberal country of the four. In reporting both left economic experts and political campaign experts, the other countries are well covered, but when it comes to Germany it is hard to find neoliberal economists on the left, and the campaign experts only come to two and one of them is McKinsey in the US. The problem goes further with Germany since Helmut Kohl, though an apparent neoliberal, had tough sledding getting neoliberal policies passed through the Bundestag. Further, other Chancellors did not revoke worker power in revoking codetermination on corporate boards, and elected works councils in firms along with larger scale trade unions. Another issue is the use of active labor market policies in periods 2 and 3. Clearly, Keynesian policies operated directly to create job training, job placement and job creation policies. While they were cut in the US, they continued to function in Sweden and Germany, though at a smaller level. Because of this, she misses the role of economists to invalidate claims for job creation based on substitution effects, which is an important part of neoliberal ideology. While all these countries may have moved towards neoliberalism in their left parties, some countries moved much further than others did. Here it would be helpful to see the scores for all four countries to see exactly where they moved. I suspect it moved much less than the others despite the Hartz IV reforms, which pale in comparison to the deep cuts in the welfare state in the US.