Game Theory and General Conference 2019

Today's post is by UM & Global blogmaster Dr. David W. Scott, Director of Mission Theology at the General Board of Global Ministries. The opinions and analysis expressed here are Dr. Scott's own and do not reflect in any way the official position of Global Ministries.

When the special called General Conference of The United Methodist Church convenes in St. Louis next February, they will be considering a variety of plans for how to resolve the denomination's long-standing debate around homosexuality. As many as five or more different plans may be up for consideration by this body - the One Church, Connectional Conference, and Traditional plans from the work of the Commission on a Way Forward, and the Plan of Dissolution and the Simple Plan submitted by other groups. Not all of these plans may pass constitutional muster, and there may have been other plans submitted of which I am not aware, but it is clear that there will be multiple plans set before the General Conference.

Yet because of how parliamentary procedure works, delegates will not be choosing from among all the plans at once. Only one plan at a time will be considered, and it seems reasonable that once one plan has been passed, no other plans will be considered, since the plans are mutually exclusive.

There are two additional complicating factors: First, some delegates may be willing to support more than one plan (as evidenced by non-exclusive voting at the Global Young People's Forum). Yet their willingness to support more than one plan might not be equal. That is, they may have a first preference and a second (or subsequent) preference that they would be willing to consider, but only if their first preference is not available.

Second, with each subsequent plan voted on, the threshold for support decreases. There was be great pressure on delegates to approve something, and the odds that delegates' first choice plan becomes unavailable and therefore they would be willing to support a second or third choice plan increase with each subsequent defeated plan. Thus, delegates would likely become more willing to vote for a plan if it is considered later in the process (assuming, of course, that no previous plan is approved and there is a later in the process).

This leads to a game theory question: If supporters of a particular plan were able to choose the order in which the plans were voted on, what would be the most advantageous order for their plan?

At first it might seem that the obvious question would be that supporters would want their plan voted on first, since then there would be no chance of another plan passing first. But the answer is actually more complicated than that and depends upon the perceived level of support for the supporters' plan and other plans.

If supporters are confident that their plan would pass as the first plan voted on, then it would make sense for them to seek to bring that plan to a vote first.

Likewise, if supporters of a plan think there is a decent though not certain likelihood that their plan will pass but also a decent (or greater) likelihood another plan would pass (remember, it is possible for people to support more than one plan and thus possible for more than one plan to have sufficient support to pass), then it would make sense to want their plan to be first, even if they were not certain they had sufficient support. It is probably better to gamble on winning in the first round rather than gambling on not losing the first round and then gamble on winning, even if the odds of winning increase somewhat if they do not lose on the first round (i.e., have another plan approved).

On the other hand, if supporters of a plan were not confident that they had the initial votes to pass their plan, but were confident that other plans also lacked sufficient votes to pass, then it would actually be advantageous to them to bring other plans up for a vote first, expecting those plans to be defeated. Those defeats would lower the threshold for support for their own plan and increase the number of people supporting their plan as a second or third choice, thereby raising the odds of their plan being passed in a subsequent round of voting.

Of course, the challenge for this game is that players operate with incomplete knowledge. Supporters of a particular plan will have estimates of the level of support for their plan and for others, but these estimates may be incorrect, making their strategy ineffective. That is basic feature for most game theory problems, though - players must operate with incomplete knowledge.

Furthermore, while this game theory analysis has assumed that players may select the order of voting, in real life, that order will be just as contested as the plans themselves. Nevertheless, I hope this piece will help readers understand the procedural conflicts about the order of business before the General Conference that are likely to precede voting on any of the actual plans.