The Predictioneer’s Game: Using the Logic of Brazen Self-Interest to See and Shape the Future

by Bruce Bueno De Mesquita

  That’s right, understanding and shaping the process by which a CEO or other leaders are chosen can tip the competition in your favor. It’s funny that few of us pay much attention, in a strategic sense, to something as prosaic as how votes are counted, whether in the boardroom or national elections. And yet the method used to translate what people want into what they get can turn a losing candidacy into a winning one.3

  When I talk about shaping outcomes based on voting, I don’t mean anything like miscounting or cheating. I don’t mean relying on hanging chads or anything like that. I’m just thinking about the many regular, commonly used ways of arriving at a choice based on what voters or shareholders or board members want.

  Few board members or shareholders pause to think about how the votes are going to be counted when they select a new CEO. Hardly anyone asks whether it really matters if we require a candidate to get a majority or a plurality; if we count just votes for people’s first choice or we allow them to express their first and second (or even more) preferences; if in decisions with many candidates we vote on all of them at once or we pair them up in head-to-head contests. And yet you can bet your bottom dollar that these decisions really can change the results.

  Just think back to the hotly contested 2008 Democratic Party primaries. The Democrats allocated delegates from each state roughly proportionally to the candidates based on their share of the popular vote in each primary. Barack Obama won a majority of delegates that way, and was ultimately elected president. If the Democrats had used the Republicans’ winner-take-all rule in each primary, Hillary Clinton would have won enough delegates to be the nominee, and she too probably would have gone on to beat John McCain. That’s a pretty big consequence of a seemingly inconsequential rule.

  There is, of course, no right way to count votes. Every method has advantages and disadvantages. So we might as well use voting rules when we can to help the candidates we favor. Generally we don’t have the opportunity to change how votes are counted in government elections, but we sure do when it comes to corporate decisions.

  In fact, I’ve twice used the range of boardroom voting procedures to help shape corporate choices of CEOs. Once the effort was entirely successful, and the second time, well, the candidate that my partner and I helped rose from obscurity to be treated as a very serious candidate. He ultimately lost, but he did so much better than anyone expected that he was quickly hired away from his company to become the CEO of a different firm—and he was a great success there.

  How was the CEO selection process modeled? Let’s take a look at my first experience on this front (it has the nice feature that even the person who was chosen as CEO didn’t know—and probably still does not know—how he won). Here’s what happened:

  The retiring CEO of the company in question—certainly it must be obvious that there is a need for anonymity here—didn’t have strong feelings about who he wanted to replace him. He did, however, have very strong feelings about who he did not want to replace him, and it just so happens that the person he didn’t want was the leading candidate for succession. The retiring CEO truly despised this person, who had been his nemesis for many years, and he hired me in secret to help engineer the CEO selection. The modeling job: figure out how to beat the detested front-runner.

  As with any analysis, the first step was to figure out just what were the real issues that had to be resolved. In this case, the big questions were simple enough. They required working out who the prospective candidates were and how they stacked up against each other. Let’s call the candidates Larry, Moe, Curly, Mutt, and Jeff—with Mutt being the guy to beat.

  The problem was best analyzed with a bunch of beauty contests. Each beauty contest asked how the stakeholders with a say in selecting the CEO felt about Larry vs. Moe, Larry vs. Curly, Larry vs. Mutt, Larry vs. Jeff, Moe vs. Curly, and so forth.

  Once the issues—the beauty contests—are specified, we need to know each stakeholder’s position, or which candidate he or she favors in each head-to-head contest, and by how much. (I will go into further detail in subsequent chapters as to the particular methodology behind these assessments.)

  Thankfully, in this particular case, we have a good source of information: the outgoing CEO. He knew who the players were and he knew how they felt about each candidate. And you can be assured he didn’t get to be CEO without knowing which of his colleagues had real clout and who would just go along with the wishes of others.

  The existing procedure for succession in the CEO’s company did not involve head-to-head contests, ranking of candidates, runoffs, or a host of other common voting rules. Instead, they normally voted for all the candidates simultaneously, just as is done in American presidential elections. Whoever got the most votes would be the winner. Now that would have been very bad news for my client, the retiring CEO. It was clear that such a procedure, a fine, upstanding, legitimate procedure, would result in the election of Mutt, the detested candidate. What to do?

  The first thing was to sort out who was likely to win each of the beauty contests. The stakeholders consisted of the members of the company’s CEO selection committee. Let’s say the committee was made up of fifteen individuals, with one vote each. The outgoing CEO’s information on the comparisons of candidates in pairs allowed me to tease out the strict order in which different committee members preferred the candidates. It was apparent that the fifteen committee members divided equally into five voting blocs based on their preferences, with three members in each group. Here are the five different preference orderings held by the members of the selection committee, with candidates listed from most preferred to least preferred:

  Mutt, Jeff, Larry, Curly, Moe

  Mutt, Moe, Curly, Larry, Jeff

  Moe, Mutt, Curly, Larry, Jeff

  Jeff, Moe, Curly, Larry, Mutt

  Larry, Jeff, Curly, Moe, Mutt

  In a contest in which everyone got to vote just one time, such as is used in the United States to pick the president, the detested Mutt would get 6 votes (two blocs held him in first place and each had three members), Moe 3, Jeff 3, Larry 3, and poor Curly 0. Mutt wins. That is exactly what had to be prevented.

  However, under another voting system, if committee members got to cast 4 votes for their first choice candidate, 3 for second, 2 for third, 1 for fourth, and no points for their last choice (a method known as a Borda count), then Mutt and Moe would receive 33 weighted votes each, Jeff would get 30, and Larry and Curly would bring up the rear with 27 each. If they then held a tie-breaking runoff between Mutt and Moe, Moe would pick up the votes of the third, fourth, and fifth blocs. They each favored him over Mutt. Moe would be the new CEO by this procedure.

  So already we can see that there is a rule that could beat Mutt. However, it was clear enough that this procedure would be tough to get through the committee. It was just too complicated to ask members first to rank candidates and then to hold a runoff once they discovered there was a tie. Such a convoluted election process would easily arouse suspicion among committee members. They might have wondered why the retiring CEO was asking them to do something so elaborate when they could just vote straight up for any candidate they wanted.

  Even if this complicated procedure could get committee approval, we would not have been home free. The procedure itself might be thwarted if a Mutt supporter caught on. For instance, if even one member of the second bloc worked out the results ahead of time, that member—who really wanted Mutt—could strategically (that is, by lying) decide to rank Jeff second and Moe last. Sure, that would have been a misrepresentation, but then the voter’s interest was in the final choice, not any intermediate decision. Acting strategically by inflating Jeff’s ranking, the bloc member would have ensured that Moe’s total in the rankings would come to 30 instead of 33, and so would Jeff’s, greatly complicating the process by creating a tie for second place and increasing the odds that Mutt would win. After all, in a runoff against Jeff (likely since more blocs preferred Jeff to Moe than the other way around
), Mutt would be the winner. By acting strategically, then, it was possible for one or more members of the second bloc to ensure the election of their most preferred candidate, the detested Mutt. That was a chance I wasn’t willing to take. Instead I decided to get Curly elected.

  Poor Curly—he was at a huge disadvantage. No one viewed him as their first-place choice. Nobody even thought of him as second choice. In fact, he was barely on anyone’s radar screen. I know that for sure because after working out how to get him elected, I had a conversation with a member of the selection committee. My role in the process was a secret, known only by the then CEO and me. I asked the committee member who he thought would be chosen, and he mentioned Mutt and maybe Moe. I nonchalantly asked about Jeff, Larry … and Curly. He took Jeff and Larry seriously, although he didn’t think they could win. Then he told me that neither he nor anyone else on the committee understood why Curly had put himself forward. After all, he said, he just doesn’t have a prayer, no one favors him. Sure, they liked him well enough, but they just didn’t seem to think of him as CEO material. Curly’s relative obscurity was, in this case, his great advantage. It was unlikely that anyone paid enough attention to Curly’s candidacy to maneuver strategically to thwart his prospects, since they didn’t think he had any.

  Okay, so now the fun begins. The outgoing CEO was well liked and highly respected. He had done a good job. The beauty contests revealed enough to show how to get Curly elected (do you see how?), but I needed to analyze one more issue first. The question was whether the retiring CEO had enough clout to persuade the selection committee to follow the winning voting procedure. The analysis of that question showed that indeed he could get the committee to follow the voting rule he suggested, provided it wasn’t too complicated. Fortunately, the procedure my analysis suggested was an eminently reasonable rule. It wasn’t particularly complicated, and it capitalized on the committee’s majority not being keen to elect Mutt in the first place (remember, he had 6 first-place votes; 9 first-place votes were distributed among the others).

  Agenda control—determining the order of decision making—can be everything. In this case it was. By setting the right agendas we could create a series of winning coalitions, each made up of different members from the one before, ending with a winning coalition supporting Curly and leaving no other candidate up for consideration.

  The committee members understood that the real contest was between Mutt and Moe—or so they thought. To reinforce their view, the outgoing CEO persuaded the committee to use an agenda—a sequence of choices—that was made up of a specific sequence of head-to-head elimination contests. Of course there were too many candidates to ask the committee to compare each candidate to each other candidate, two at a time. That would have meant ten votes. Instead, the retiring CEO persuaded the committee to vote on Mutt versus Moe, with the loser of that contest being eliminated from consideration and the winner then going up against Jeff. Whoever lost that contest would be dropped from consideration, and the winner (who at this point in principle could have been Mutt or Moe or Jeff) would then be voted on against Larry, and the winner of that vote would finally be voted on against Curly. Whoever was left standing after those four votes would be deemed the winner.

  This seemed like a good idea to the selection committee. They thought that by leading with strength—Mutt vs. Moe—they would quickly arrive at the one of those two who overall was most desired as CEO. How wrong they were. To be sure, anyone paying close attention to the five voting blocs’ preferences could have worked out how the retiring CEO’s agenda would work out, but it was unlikely that the committee members knew the full preference ordering of their compatriots. They, after all, were unlikely to conduct the sort of expert interviews called for by the model. Since they weren’t asked to announce their candidate rankings, the rule proposed by the retiring CEO did not compel them to reveal to each other their full ranking of candidates. Probably on their own they had not probed one another beyond second-place preferences. That, presumably, was why they paid so little attention to Curly. So here is what happened:

  Moe beat Mutt right off the bat—by a vote of 9 to 6 (blocs 1 and 2 voting for Mutt and the rest voting for Moe, as you can see from the rankings listed earlier). Mutt, being the loser, was dropped from consideration under the seemingly reasonable supposition that more people wanted Moe than Mutt (9, as we saw, to 6). Fair enough. Everything after that was gravy, because my client’s main concern was to beat Mutt. But then my client also liked the idea of choosing Curly. He thought that would make him look even better in retrospect, and besides, he was fond of Curly and thought being CEO would be a nice way to cap Curly’s career.

  The selection committee then considered Moe and Jeff in accordance with the agreed-upon agenda. Jeff beat Moe as handily as Moe had beaten Mutt. Bloc 1 wanted Mutt most of all, but now, confronted with a choice between Moe and Jeff, they went for Jeff. He was their second-place choice, while Moe came in last for bloc 1. Blocs 4 and 5 also thought Jeff was a better prospective CEO than Moe. Only blocs 2 and 3 favored Moe over Jeff. That gave Jeff 9 votes to Moe’s 6. Mutt having already been eliminated, no one on the committee stepped back to ask what would happen if they took the opportunity to choose between Jeff and Mutt. As you can see from the bloc preferences, there was yet another winning coalition (blocs 1, 2, and 3) with whose support Mutt would have beaten Jeff, but again, Mutt had been taken out of the picture by Moe in accordance with the elimination rules agreed to.

  Mutt and Moe, the apparent front-runners, were now out of the race. Moe beat Mutt, and Jeff beat Moe. Jeff, Larry, and Curly were still standing. Jeff and Larry each had first-place supporters, so they were run against each other next. Blocs 2, 3, and 5 favored Larry over Jeff. Jeff was out, leaving a final choice between Larry and Curly. Of course you can easily see that Curly is going to defeat Larry. Blocs 2, 3, and 4, in the ever-shifting winning coalition of voters, favored Curly over Larry. Curly, being the last man standing, was the new CEO much to (almost) everyone’s surprise. Still, they felt the process had been fair and square, and in its own way it was.

  No one seemed to notice that the agenda had decided the outcome. It so happens that Larry was the only candidate that Curly could have beaten. If the agenda had been different, Curly would have lost. Just as Curly could not beat anyone other than Larry, so too could Larry not defeat anyone other than Jeff. Moving Larry up in the agenda would have wiped him out and Curly with him. In fact, because preferences went around in circles (or, to put it technically, they were intransitive), an agenda could be put forward to make any of the candidates into the winner fair and square.

  When the vote was over, the committee member with whom I had talked earlier invited me to lunch. He had one question for me: Did you have anything to do with picking our CEO? I smiled and changed the subject. He was sure I did, and I knew he knew, but I was sworn to secrecy. The lunch was great.

  SORRY, EINSTEIN: GOD DOES ROLL THE DICE

  As we see in moving from the prisoner’s dilemma to the bank example to the voting strategies, even in relatively simple games involving relatively few players there can be multiple outcomes. This fact adds yet another strategic dimension to decision making, particularly as games, in the real world, are often played over and over between the same players.

  Any time a game has more than one possible result, there is a special type of strategy (called a mixed strategy) that can influence what happens. In a mixed strategy, each player chooses actions probabilistically—say, by rolling dice—to influence what other players expect to get out of the game. Einstein’s God may not have played dice with the universe, but we mortals definitely roll the dice with each other.

  Whenever you watch a football game and complain about a coach’s choice of plays, you probably were watching a mixed strategy at work. For instance, when the ball is on the one-yard line, the play that is most likely to get the ball across the goal line is for the fullback to jump over the pile of players in front of him. Yet co
aches often have the quarterback pass the ball or hand off to a running back. The reason: if a coach always called for the fullback to go over the top, the defenders would concentrate the defense at that point, and the play would probably fail. By mixing the calls, the offense forces the defense to spread out, thereby improving the odds of success over repetitions of the situation. Interestingly, this sort of mixing of strategies carries important lessons for business, politics, and lots of other parts of life. Rolling the dice is one way to alter how other people perceive a situation.

  Using strategies that involve mixing up moves to create a change in expectations is something that comes up all the time. Although applied game theorists often like to ignore these complicated “mixed strategy” approaches to problems, they do so at their own peril. Rolling the dice can really make a difference in how things turn out.

  Examples of such gambling are all around us, and some great movies roll the dice very cleverly to create climactic moments. Who can forget in The Princess Bride the back-and-forth over which wineglass is poisoned, and the clever resolution (both were poisoned—it pays to build up an immunity to the poison you plan to use on yourself and others). Or how about the fabulous scene from The Maltese Falcon in which Sydney Greenstreet’s character, Kasper Gutman, desperately wants the jewel-encrusted bird? Only Sam Spade (Humphrey Bogart) knows where it is, and Sam Spade is no fool. Gutman threatens that Joel Cairo (Peter Lorre) will torture Spade to find out where the bird is, but Spade counters, “If you kill me, how are you going to get the bird? If I know you can’t afford to kill me till you have it, how are you going to scare me into giving it to you?” Here Spade, like any good game theorist, questions the credibility of Gutman’s commitment to make him talk. We know and Sam Spade knows that, without a real commitment to kill him, Gutman can’t get him to talk. But Gutman is no fool either. He knows just how to make the dice tumble, creating the prospect that Spade will talk to save himself. After some clever give-and-take, Gutman retorts, “As you know, sir, men are likely to forget in the heat of action where their best interests lie and let their emotions carry them away.”