A plausible hypothetical regarding Sanders and Bloomberg

[Act_of_Reparation]

13. Anecdotes.

Given a symmetric configuration of candidate positions, if uncertainty about the general election results at the time of the primary election is high, then the open primary system always leads to an outcome that is at least as moderate as the outcome under the closed primary system. Even when uncertainty is low, if the extreme candidate in each party is sufficiently extreme, then the outcome in the primary election is never more extreme under the open system than under the closed system. However, if there is low uncertainty and the extreme candidate in each party is sufficiently moderate, the party nominees under the open primary system can be more extreme in expectation than those under the closed primary system.

Cho, S., & Kang, I. (2015). Open primaries and crossover voting. Journal of Theoretical Politics, 27(3), 351–379. https://doi.org/10.1177/0951629814531671

While tests performed have limitations, none yields strong evidence that strategic crossover voting in response to Rush Limbaugh's Operation Chaos was a widespread phenomenon. These findings therefore extend the somewhat dated literature on strategic crossover voting in response to instigation from a popular political figure. The absence of a Limbaugh effect suggests that states or parties holding open primaries have little to fear about their elections being mischievously influenced by activists from the opposing party.

Stephenson, E. Frank. “Strategic Voting in Open Primaries: Evidence from Rush Limbaugh's ‘Operation Chaos.’” Public Choice, vol. 148, no. 3/4, 2011, pp. 445–457. JSTOR, www.jstor.org/stable/41483706. Accessed 28 Jan. 2020.