In Chapter 5 of Public Choice III, Mueller writes about the possibility of cycling equilibria with majority voting under a single issue framework. Knowing that there is a possibility of cycling equilibria when there are many parties with separate utility maximizing locations, he discusses the work of McKelvey and the concept of one party controlling the voting process, leading to a better result (more utility) for them.
An interesting application of this is Chapter 11 Bankruptcy and the voting on a Plan of Reorganization proposal. Because of the unique legal structure that can "cram down" (zero out) equity and debt of a company with a 2/3 vote (most importantly not unanimous), many credit hedge funds are involved in this sector. Imagine a graph with an x1 of a recovery for one tranche of debt and x2 of another. Many different funds/creditors fight (and eventually vote) for higher recoveries, and the process is often costly and outcome possibly bad (funds get "bageled" or 0 value and -100% return), so controlling the process can be very advantageous.
In the bankruptcy for Quicksilver, hedge fund Oaktree gained control by providing Debtor-In-Possession financing for the debtor to fund its bankruptcy. I'll be brief and say that providing this form of financing gives the creditor immense legal control over the deadlines and voting procedures in a bankruptcy process. At the end of the day, Oaktree made gains on their debt claims and owned Quicksilver itself after the bankruptcy and ended up turning it around and selling it for 2-3x their principle- they made a killing, and this was made possible because they had control over voting and steered the process into a favorable equilibrium.
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