The Black Knight's, sorry, Bernie Sanders' claim that closed primaries are illegitimate gets at one of the persistent annoyances in political debate. To what degree do we care about process for its own sake, and to what degree are our preferences over process determined by our preferences over outcomes? I have already addressed the open/closed primary and Sanders specifically (here), but today, let's take a more general approach.
Electoral rules determine electoral outcomes. For any set of preferences, you can construct a process that will result in any outcome you want, if you are sufficiently creative and brazen with the rules. The manipulability of election outcomes is based on what we sometimes call "the chaos theorem" (not theory, but theorem), built on the work of Richard McKelvey. It's a bunch of math, so I'll spare you the details and just give you the executive summary. People have complex preferences. That complexity means that if you set up the choices as A versus B, and the winner faces C, that gives you a different result from A versus C, and the winner faces B. What McKelvey showed is that if you set up a sequence of choices the right way, you can get pretty much any outcome you want by exploiting the complexity of peoples' preferences. If you want the math, go read McKelvey.
... which leads us to this guy:
Or, rather, the political scientist who shared his name. One of his important observations is what we sometimes call "the heritability problem." Basically, if the process you use determines the outcome, then your preferences over process are determined by your preferences over outcome, and the choice of process is just as fraught as the choice over outcomes.
That's a bunch of jargon, but at the end of the day, what it means is this. If open primaries benefit Sanders, and closed primaries benefit Clinton, then your preference over primary rules will be influenced by your preferences in the Clinton versus Sanders contest. Should the Democratic Party be able to determine its own nominee without meddling from Republicans, or should the process be as open as possible so that you don't need to go through the bureaucratic hassle of registering as a Democrat if you decide you would rather vote in the Democratic primary? That question, in Riker's terms, is indistinguishable from your Clinton/Sanders preference.
We see this all over the place in politics. Should the federal government or state government set policy on a matter? For you, that will depend on whether you are more or less likely to get your way at the federal level. How much should public opinion influence policy? That depends on whether or not you are in the majority. Should the courts strike down laws passed by elected officials? That depends on whether or not you like the law. This is all the same.
And it's all heritability. OK, I'm done for the day. I'm out of here...