That’s the title of a paper by Michael Kremer and Benjamin Olken. The bottom line is:

…a union that implements workers’ preferences will not be evolutionarily stable.

The union that survives must either extract fewer rents for the workers (thus lowering anti-union expenditures from the employer, or helping keep the employer in business) or spend excess funds on organizing and bolstering union membership in the broader economy. A union that spends on membership and organizing drives tends to spread from one firm to the next. If a union were truly controlled by its members it would take lots of current rents with little concern for the longer-term future of the firm or for the longer-term future of the union.

Here’s a neat paragraph:

The dynamics of unionization levels also bear a similarity to those under the Susceptible-Infected (SI) model of epidemiological dynamics…In that model, new potential hosts are born uninfected; the chance that they become infected increases with the number of hosts already infected; and once hosts are infected, they stay infected until they die. Note that this comparison is purely positive, not normative.

Yes the paper does offer some evidence but it is more interesting as a theory piece. Here is an earlier ungated version, there is also 2001 version listed at NBER and here is the current version.