Negotiations within Congress as well as between Congress and Senate (and the White House) have already broken down. At this point, the fate of this crisis clearly lies in Senate. So, the question is: Which senators hold the key to breaking this deadlock? In other words, what group of senators would be able to influence at least 60 senators to vote "yes" on a deal brokered by them?
This is game theory on a grand, public display. The "players" here are the members of the two major parties in Parliament. Their actions are purely strategic. One anticipated outcome of this "game" is that a bipartisan group of senators would broker a deal in Senate. It would then be sent to Congress at the last minute to avoid the much dreaded default. The Republican-controlled Congress would have two options---either pass that deal or bear the blame for the ensuing default. Considering several recent polls that show that the public is mostly blaming the Republican Party for the government shutdown, it is likely that Congress would pass a Senate-brokered deal.
Going back to my previous question, what group of senators would be influential to brokers such a deal? One part of my PhD Dissertation actually deals with questions like these in strategic/game-theoretic settings. The general approach there was to first design a mathematical model of influence among the "players of the game" (that is, the senators in this case), then learn the parameters of the model (such as how much Senator X influences Senator Y) from the historical voting data, and finally, compute the stable outcomes (in mathematical term, pure-strategy Nash equilibria) of the game to answer such questions. These stable outcomes can be thought as potential voting outcomes in Senate.
Here, I will use that approach to evaluate the influence of various possible groups of senators on their peers. For example, as of today, intense negotiations have been going on between the Senate Majority Leader Harry Reid (D, NV) and the Senate Minority Leader Mitch McConnell (R, KY). Previously, a bipartisan plan, led by Senators Susan Collins (R, ME) and Joe Manchin (D, WV), was proposed without much success. One interesting question is: What would happen if Senators Reid and McConnell now join that bipartisan plan? Will it pass with at least 60 "yes" votes? Another interesting question is: Is there a small number of senators who could help Senators Reid and McConnell pass their deal on the Senate floor (by joining their coalition)?
According to our model, if all the democratic senators, including Senator Reid (D, NV) are predisposed to voting "yes" and if in addition, Senator McConnell (R, KY) also votes "yes," then the bill will pass for sure with at least 60 votes (i.e., there is no chance of a filibuster). However, if we don't assume that all the democratic senators are on board, then it requires a "large" body of eight influencing senators to pass the bill without any filibusters. One such influencing body of senators, according to our model is, Reid (D, NV), McConnell (R, KY), Inouye (D, HI), Johnson (R, WI), Sanders (I, VT), Conrad (D, ND), Portman (R, OH), and Collins (R, ME). This is a bipartisan group of four republican senators and four democratic (or democratic-minded independent) senators.
As statistician George Box's famously said, "All models are wrong, but some are useful," there is no way validating a model of influence like ours. However, we definitely see a lot of anecdotal evidence that our model is capturing various strategic aspects of the deals in Senate. First, our model predicts that we would need a bipartisan group of influencers that consists of roughly the same number of democratic and republican senators for making a deal in Senate. Second, in Senates prior to the 112th Senate, our model predicts that certain groups of only six senators would have been sufficient to reach a complete consensus (i.e., if those six senators voted "yes" then everybody else would also vote "yes"). An influencing group of only six senators is no longer sufficient for the 112th Senate. It requires a body of eight influencing senators just to gather 60 "yes" votes to avoid filibusters (as opposed to a complete consensus of 100 "yes" votes). Furthermore, our model also predicts that reaching a complete consensus in the 112th Senate would require an influence body of 10 senators (as opposed to six senators in prior Senates)! This certainly testifies to the general perception of polarization in Congress these days.
Going back to my previous question, what group of senators would be influential to brokers such a deal? One part of my PhD Dissertation actually deals with questions like these in strategic/game-theoretic settings. The general approach there was to first design a mathematical model of influence among the "players of the game" (that is, the senators in this case), then learn the parameters of the model (such as how much Senator X influences Senator Y) from the historical voting data, and finally, compute the stable outcomes (in mathematical term, pure-strategy Nash equilibria) of the game to answer such questions. These stable outcomes can be thought as potential voting outcomes in Senate.
Here, I will use that approach to evaluate the influence of various possible groups of senators on their peers. For example, as of today, intense negotiations have been going on between the Senate Majority Leader Harry Reid (D, NV) and the Senate Minority Leader Mitch McConnell (R, KY). Previously, a bipartisan plan, led by Senators Susan Collins (R, ME) and Joe Manchin (D, WV), was proposed without much success. One interesting question is: What would happen if Senators Reid and McConnell now join that bipartisan plan? Will it pass with at least 60 "yes" votes? Another interesting question is: Is there a small number of senators who could help Senators Reid and McConnell pass their deal on the Senate floor (by joining their coalition)?
According to our model, if all the democratic senators, including Senator Reid (D, NV) are predisposed to voting "yes" and if in addition, Senator McConnell (R, KY) also votes "yes," then the bill will pass for sure with at least 60 votes (i.e., there is no chance of a filibuster). However, if we don't assume that all the democratic senators are on board, then it requires a "large" body of eight influencing senators to pass the bill without any filibusters. One such influencing body of senators, according to our model is, Reid (D, NV), McConnell (R, KY), Inouye (D, HI), Johnson (R, WI), Sanders (I, VT), Conrad (D, ND), Portman (R, OH), and Collins (R, ME). This is a bipartisan group of four republican senators and four democratic (or democratic-minded independent) senators.
As statistician George Box's famously said, "All models are wrong, but some are useful," there is no way validating a model of influence like ours. However, we definitely see a lot of anecdotal evidence that our model is capturing various strategic aspects of the deals in Senate. First, our model predicts that we would need a bipartisan group of influencers that consists of roughly the same number of democratic and republican senators for making a deal in Senate. Second, in Senates prior to the 112th Senate, our model predicts that certain groups of only six senators would have been sufficient to reach a complete consensus (i.e., if those six senators voted "yes" then everybody else would also vote "yes"). An influencing group of only six senators is no longer sufficient for the 112th Senate. It requires a body of eight influencing senators just to gather 60 "yes" votes to avoid filibusters (as opposed to a complete consensus of 100 "yes" votes). Furthermore, our model also predicts that reaching a complete consensus in the 112th Senate would require an influence body of 10 senators (as opposed to six senators in prior Senates)! This certainly testifies to the general perception of polarization in Congress these days.
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