There has been some pushback against the claim, from our #workersparty manifesto, that min wages is sound policy. Let me begin by emphasizing a position I've held from the start: min wages is not unabashedly good policy. But it is a good start that is also evidence-based. 
In social sciences, there is seldom unambiguous evidence. Studies can yield different results, which is why continued research is important & policies should be based on the overall literature. That's why I mentioned that many papers since Card-Krueger corroborate its findings.
The best way to aggregate and evalute the totality of results is to rely on meta-analyses, which are studies of studies. Meta-analyses take the existing results out there, and ask if there are systematic conclusions we can draw from the literature. So let's look at these.
As it turns out, almost all meta-analyses for the UK and US find little or no employment effects from min wages. The outlier is Neumark-Wascher. So, much like studies on anthropogenic climate change, the evidence mostly points in one direction, but it isn't unanimimous.
Very recent studies also tend to support the notion that min wages generate little employment effect, even for low-wage workers, and even when the jump is quite substantial. This is the main takaway from studies of Seattle's recent min wage ordinance (doi.org/10.3386/w25182).
Of course, there are country-specific idiosyncrasies. That's why before rolling out such a policy here, it is crucial that we have an evaluation framework in place, and an independent min wage-setting board, which can make on-the-fly adjustments in response to local conditions.
Who pays for the minimum wage? Some people think this would cost the government. Actually, most min wage models have no fiscal impact, and the burden is borne mostly by higher prices consumers pay (3/4), and in part by firms (1/4) (doi.org/10.1257/aer.20…).
I see this as a feature, not a bug. The point is to redistribute some bargaining power from capital to labor, and I think we can afford to chip in a little to take care of the least well-off in society. With many more buyers than min wage workers, the price effect will be small.
One final point: some have suggested that the Progressive Wage Model (PWM) rolled out by the govt, is (in effect) a min wage. I don't agree. The PWM ties wages to job function, which still gives too much room to employers to cut corners, without redressing power differentials.
It also leaves those who simply cannot upskill in the lurch, and earning below a living wage. The reality is that, by our estimates, 100,000 workers remain below the min wage, and so PWM is obviously not working for these people.
Cites: For the UK, see de Linde Leonard, Stanley & Doucouliagos 2013 (doi.org/10.1111/bjir.1…), Dube 2019 (assets.publishing.service.gov.uk/government/upl…), Hafner et al. 2017 (rand.org/content/dam/ra…).
More cites: For the US, see Card & Krueger 1995 (jstor.org/stable/2117925), Doucouliagos & Stanley 2009 (doi.org/10.1111/j.1467…), Neumark & Wascher 2008 (mitpress.mit.edu/books/minimum-…). For international evidence, see Boockmann 2010 (ftp.iza.org/dp4983.pdf).
Postscript: In case you're wondering about the comic in the first frame, it's from the always-insightful xkcd. The specific entry is here: xkcd.com/386/
