Running for Higher Office: Case Studies

Puzzle: When will a member of the House of Representatives decide to run for Senate over for Governor?

"Political ambition" generically refers to either (1) a politician holding office deciding to run for a higher office, or (2) an individual who does not hold a political position to run for office.

Aldrich and Bianco note that when political ambition is cast in "utility maximization terms" (which I will extend from decision-theoretic framework to include game theoretic ones), it is called a Calculus of Candidacy. This is in analogy to Riker and Ordeshook's term "calculus of voting".1 See W.H. Riker and P.C. Ordeshook, "A theory of the calculus of voting" American Political Science Review 62 (1968) pp. 25–43; or their follow up book An Introduction to Positive Political Theory, Prentice Hall, 1973. As a decision theoretic problem (i.e., ignoring adversaries), it may be cast as maximizing the expected utility: \[EU(a_{k}) = \sum_{j}P_{jk}U(O_{k}) - C_{k}\] where \(a_{k}\) is the strategy of pursuing action \(k\), \(P_{jk}\) is the probability of outcome \(j\) given action \(k\), and \(C_{k}\) is the cost of taking action \(k\). The rational action then chooses the strategy which maximizes the expected utility of its outcome.

But how is this process exactly done? Is there any interaction with "party elites"? Does a person just wake up one day, and announce, "You know what? I think I'll run for governor starting today, because my expected utility of that course is maximized"? And is decision theory the right tool — will potential candidates need to consider potential primary challengers or the potential of defeating an incumbent? Aaron King's doctoral thesis examines these questions on the dynamics surrounding political ambition in greater detail.

This post will gather a few case studies, in preparation for future work trying to set up a game theoretic model for political ambition.

Case Studies

Case Study: Michael Punke and Montana's 2020 Governor Race. The initial decision to run, however, seems to involve some communication with "party elites", as Politico reports about Michael Punke considering a run for Montana's governorship (and the ambitions of Governor Cooney and Mayor Collins):

Punke, who has talked to leading Montana Democrats about his political ambitions but is not talking to donors at this stage, has described himself to potential backers in Montana as "rabidly centrist" and said that if he runs, he would likely focus on issues like health care and workforce development, said one source. He would also use his WTO trade experience as a selling point because some of Montana’s biggest industries are trade-dependent, like exports of agricultural products and copper and even tourism.

[...] The current Democratic governor of Montana, Steve Bullock, is term-limited and is expected to announce a run for president soon. Independent Helena Mayor Wilmot Collins and Democratic Lt. Gov. Mike Cooney are also seen as potential candidates for governor, though Collins said in March he was also considering the Senate race and appears ready to launch a campaign for that office.

The inferences we should draw from this reporting is: (1) there are "party elites" whom Michael Punke is courting prior to entering the race, (2) the considerations of possible opponents are taken into consideration in each actor's calculations.

Curiously, similar processes appear to unfold in the Republican side of the Montana senate race.2 DailyKos's daily election digest reports, MPR's Brian Bakst reports that Bill Guidera, a former executive at 21st Century Fox and News Corp, is considering seeking the GOP nod to take on Democratic Sen. Tina Smith. Guidera, who used to serve as the Minnesota Republican Party's finance chairman, doesn't appear to have said anything publicly yet, but Bakst acquired an email from someone he identified as a longtime friend and quasi-adviser who said that Guidera is thinking about running and holding a fundraiser. Bakst also adds that Guidera has been appearing at local GOP events and doing meet and greets.

We should caution the reader that some sources, e.g., Daily Kos Elections, have used the phrasing of a candidate "seeking the nod from the party" as synonymous for "has entered the primary to be the party's nominee" for an office.3 For an example of this poor abuse of language, DailyKos's daily election digest reports, Former Gov. Bill Haslam confirmed this week that he is still considering seeking the GOP nod to succeed retiring Sen. Lamar Alexander, and he told WBIR that his decision could come as early as next month. To the best of my knowledge, and all the sources I could find, there is no discussions between Governor Haslam and the Tennessee GOP party elites.

Case Study: Bill Weld's 1996 Senate Decision.4This example is inspired from Kenneth A Shepsle's Analyzing Politics, first ed., pages 22–24. First elected in 1991 as governor of Massachusetts, Bill Weld's gubernatorial term came to an end with the November 1994 election. A popular Republican governor in a famously liberal state, Weld remedied the financial debts through a well-executed political squeeze play (thwarting the state legislature from borrowing more money or raising taxes with veto threats), restructuring the state's debts, and taking advantage of Medicaid loopholes to acquire $500Mn from the federal government. The sordid details and play-by-play are well documented in Richard Hogarty's Massachusetts Politics and Public Policy.

Weld was popular inside the state, and outside. It was whispered that party elites were entertaining the idea of Weld as the presidential or vice-presidential candidate in 1996. The governor was inevitably aware of these rumors, since the New York Times's conservative pundit William Safire endorsed such an idea in his 1993 op-ed piece What about Weld, which could be sustained by holding public office. (If you don't know who Mr Safire is, please read Rick Perlstein's Nixonland; it's a wonderful book, and explains only parts of Mr Safire's connections with, and sway among, conservatives and Republican party elite.)

But, things were not so straightforward. Senator Ted Kennedy's term was coming to an end, and Sen Kennedy faced re-election in the November 1994 election as well. Or retirement. In his term, Sen Kennedy faced a number of contraversies ranging from his personal life to his handling of Clarence Thomas's nomination to the supreme court. The GQ's 1990 profile, Ted Kennedy on the Rocks, did little to help. The Boston Globe later reflected, Not surprisingly, many thought the senator would announce that he wasn't running for reelection in 1994, that it was time to get his personal house in order. In fact, Kennedy was already gearing up for the toughest race of his Senate career. The senator announced his intention to run for re-election early in Spring of 1994, entering the race as an especially disadvantaged incumbent.

Governor Weld could either risk challenging the vulnerable Sen Kennedy for the senate seat or run for re-election as governor of Massachusetts. Political observers agreed any race between Kennedy and Weld for the senate would be a toss-up,5For example, The New Republic reported there were more independent voters than registered Democratic voters in 1994. There is a big bloc of voters, as high as 40 percent of the electorate, that is no longer available to Kennedy, a Boston pol who is advising the senator's campaign confided. If anyone runs a minimal campaign, he'll get at least that much of the vote. Such, at least, was the specious reasoning of political operators at the time. but the governor's race would be a lock. Regardless of the choice, Weld needed to hold one of these offices to be considered as presidential (or even vice-presidential) material.

Framed thus, we would expect the decision Weld would make should be to run for re-election as governor in 1994, and enjoy a chance to join the GOP's ticket for the 1996 presidential race.

Well, Weld did run for re-election in 1994, winning 71% of the popular vote. A year afterwards, on November 29, 1995, the governor made his intentions clear to run in 1996 against the junior senator John Kerry after securing the blessings of financial backers and GOP party elites.6The only source I could find documenting this was the Boston Herald's article, Weld expected to launch bid today dated November 29, 1995. Curiously, the article notes, Weld advisers also noted that Weld came to the brink of the presidential race and the 1994 Senate race before bowing out.

Further, that article notes how Weld secured the blessings of Republican donors and party elites: Weld, who was scheduled to be in Manhattan this morning to meet with campaign fund-raisers, reserved a hotel function room in Boston this afternoon in anticipation of announcing his entrance to the race. [...] Today's New York meeting is one last step toward a possible Weld candidacy. New York has been an important factor in the Weld fund-raising equation — accounting for as much as 15 percent of the $6.5 million Weld raised between the 1990 and 1994 gubernatorial elections. While this morning's breakfast was depicted as a critical factor in Weld's decision, a negative outcome is unlikely. Sources close to Weld noted that the people attending the New York event include the governor's two brothers, his sister, and former Harvard classmates. [...] According to sources, Weld has already begun to assemble a fund-raising team, a critical issue since his longtime chief fundraiser, Peter J. Berlandi, has opted for a limited-duty role in the Senate race. According to sources, two Boston attorneys — Weld campaign treasurer Sandy Spaulding and 1992 congressional candidate Michael Crossen — are likely to assume key roles. Sources also said veteran Bay State GOP fundraiser Priscilla Ruzzo, a staffer for the National Republican Senatorial Committee, may be "loaned" to Weld during a startup phase. (LexisNexis saved the article, and I quote from LexisNexis's saved transcript, which may very well be in error.) The Atlantic summed up the elite opinion, Is it the wrong race? Is it the wrong year? Is Kerry the wrong target? The right race, this theory goes, was the last Senate race in Massachusetts. The right year was 1994. The right target was Senator Edward M. Kennedy.

Puzzle. What interactions occurred between election day 1994 and November 25, 1995 which led Weld to prefer challenging Sen Kerry over alternative actions?

Case Study: Claire McCaskill's Senate Run.7This example is inspired from Kenneth A Shepsle's Analyzing Politics, second ed., pages 21–23. Shepsle cites Jeff Goldberg's Central Casting article from The New Yorker, too. Claire McCaskill after graduating law school in 1978 began practicing law until she ran and won a set in Missouri's state House of Representatives. She then ran for Kansas city's county prosecutor in 1988 and won, ran for state auditor (which she viewed as a stepping stone towards governorship) in 1998 and won. Then, in 2004, McCaskill primary challenged the sitting Democratic governor Bob Holden. And won...the nomination. Alas, Roy Blunt (the Republican nominee) prevailed in the governor's race. But McCaskill defeating a sitting governor in the primary was historically unprecedented in Missouri.

But, The New Yorker informs us, In 2006, the two senior Democrats in the Senate, Schumer and Harry Reid, persuaded her to run against a Republican incumbent, Jim Talent. Her timing was good: President Bush’s dismal approval ratings helped the Democrats pick up enough seats to win majorities in both houses of Congress. McCaskill won a narrow victory. (McCaskill claims this as well in her memoir, Plenty Ladylike: A Memoir.)

Observation. "Elder statesmen" of the party [e.g., Reid and Schumer] seemingly count as "party elites" for certain races, like for the Senate.

But in 2014, Sen McCaskill considered running for Governor in 2016 instead of re-election for Senator in 2018. It had been a dream, for Claire McCaskill, to be governor of Missouri, ever since she was in high school. The New Yorker put it this way: By the time McCaskill was in ninth grade, at Hickman High School, in Columbia, she had set her sights on becoming the first female governor of Missouri. Whether this dream was real or imagined, the source or an excuse of, McCaskill's ambition for governorship was evident at the time.7The New York Times reported after the 2018 election, The loss likely marks the end of life in public office for Ms. McCaskill, a singular figure in Missouri politics who began her public career more than three decades ago in a male-dominated State Capitol and outlasted most of her Democratic peers. She has long coveted the state’s governorship, having narrowly lost a bid in 2004, but on Tuesday night, she signaled that she had run her final race, though she said she would be unencumbered in speaking her mind. (emphasis added)

The New Yorker noted about McCaskill's initial run, In 1998, McCaskill ran for state auditor, an office that she saw as a stepping stone to the governorship. And later in that same article, As recently as 2015, she considered returning to Missouri for another try at the governorship. Her mind naturally goes to practical details rather than to big concepts. Her idea of governing is to spend money wisely, punish misbehavior, and give people what they need in order to get through their daily lives.

Whether Sen McCaskill had greater ambitions beyond the governor's mansion remains as unclear as how McCaskill's ambitions evolved over time.

Ultimately, McCaskill sat down and did the calculus sometime in Winter of 2014–2015, and concluded in January 2015 that, for the trajectory McCaskill had in mind, running for re-election in 2018 was more optimal than running for Governor in 2016.8 McCaskill told KCUR in an interview in January 2015, At the end of the day, you have to ask yourself if the job you're thinking about going for is better than the one you have, and can you do more? She reaffirmed this stance with St. Louis Public Radio on January 15, 2015 and with Politico on January 12, 2015.

Puzzle. Did Claire McCaskill plan with Missouri state party elites or her colleagues in the Senate? Or did she arrive at this conclusion on her own?

Conclusion

We have examined a few "case studies" in political ambition. Our case studies have been "broad" rather than "deep": we had a writer aspire for governorship, a governor challenge a sitting senator, a senator with frustrated aspirations for governorship. For completeness, we should also consider a state legislator with ambitions for (1) the House of Representatives, (2) governorship, (3) Senate. But also we should consider individuals with presidential ambitions.

Fowler and McClure's Political Ambition (1989) examines a single congressional district with an open seat, specifically how state legislators determine whether to run for that open seat or not. (This is an example of a "deep" case study which is not "broad".)

We also didn't examine sufficient cases to see if the examples given are a sufficient representative sample. The gender and race of the candidates may impact the dynamics. RL Fox investigated the impact of gender on political ambition.

Although we are critically dependent on newspaper reporting, we have tried to identify a few of the key elements in the decision to run for higher office. The flaw with this approach is obvious: we lack information about "behind the scenes" interactions among key actors. But I'm not a journalist or a political scientist: I don't have the time, energy, or patience to do the investigative dirty work.

Future work could include setting up a game theoretic model of political ambition, further case studies, and possible ways to empirically test various aspects of political ambition or at least determine indicators of political ambition.

References

• John H. Aldrich, William T. Bianco, "A game-theoretic model of party affiliation of candidates and office holders". Mathematical and Computer Modelling 16 (1992) pp. 103–116, doi:10.1016/0895-7177(92)90090-8
• G. Black, "A theory of political ambition: Career choices and the role of structural incentives". American Political Science Review 66 (1972) pp. 144–159
• Scott Gates and Brian D. Humes, Games, Information, and Politics: Applying Game Theoretic Models to Political Science. University of Michigan Press, 1997. See esp. ch. 3.
• Linda Fowler and Robert McClure, Political Ambition: Who Decides to Run for Congress. New Haven, CT: Yale University Press, 1989.
• David Rohde, "Risk-bearing and progressive ambition: The case of members of the United States House of Representatives". American Journal of Political Science 23, 2 (1979) pp. 1–26 [jstor]

"Thick Description" Reading

• Why Would Anyone Ever Want to Run for Congress?, The Atlantic; April 19, 2013
• Who Wants To Be A Senator? Not These High-Profile Democrats, FiveThirtyEight; May 9, 2019
• Richard Hogarty, Massachusetts Politics and Public Policy. University of Massachusetts Press, 2002.
• A Race Too Far?, The Atlantic; August 1996
• Ted Kennedy on the Rocks, GQ; April 15, 2016
• Peter S. Canellos (ed.), Last Lion: The Fall and Rise of Ted Kennedy. Simon & Schuster, 2009.
• Stormin' Mormon, The New Republic; November 7, 1994
• Weld expected to launch bid today, the Boston Herald; November 29, 1995, pg 1.
• Central Casting: The Democrats think about who can win in the midterms-and in 2008, The New Yorker; May 21, 2006
• Claire McCaskill’s Toughest Fight, The New Yorker; October 22, 2018

Initial Decision to Run

• RL Fox, JL Lawless, "Gaining and losing interest in running for public office: The concept of dynamic political ambition". Journal of Politics 73, no. 2 (2011) 443-462. Eprint.
• Aaron S. King, Unfolding Ambition in Senate Primary Elections: Strategic Politicians and the Dynamics of Candidacy Decisions. Lexington Books, 2017. Appears to be a cleaned up version of King's doctoral thesis.
• Jennifer L. Lawless, Becoming a Candidate: Political Ambition and the Decision to Run for Office. Cambridge University Press, 2012.
• Daniel Markham Smith, Succeeding in Politics: Dynasties in Democracies, PhD Thesis at UC San Diego, 2012.

Common Knowledge of Rationality + Consistent Alignment of Beliefs = Common Priors

Heap and Varoufakis summarize the last assumption of game theory's axiomatization of rational behavior in the "consistent alignment of beliefs" axiom: no instrumentally rational person can expect another likewise rational person who has the same information to develop different thought processes.

This is usually justified by the Harsanyi doctrine: when two rational people examine the same information, they must draw the same inferences, and independently come to the same conclusion.

Robert Aumann fiercely defended this principle in his article "Agree to Disagree" (1976) and his earlier article "Subjectivity and Correlation in Randomized Strategies" (1974).

Aumann argues, if you assess it is going to rain tomorrow with 75% probability and I assess it will rain tomorrow with 33% probability, then we must have different information and we should update our probabilities accordingly until we converge on some shared probability estimate. That is, through dialogue, we (as rational actors) will arrive at a conclusion we both agree upon.

When we combine "consistent alignment of beliefs" with the common knowledge of rationality, we end up with common priors (i.e., a source of beliefs). The connection is this: if you know you are rational and you know your adversary is rational and (using consistent alignment of beliefs) you know your thoughts about what your adversary might be doing have the same origin as your thoughts about your own actions along the same line as your adversary's thoughts, THEN you adversary's actions will never surprise you. Beliefs are consistently aligned in the sense, if you actually were able to know your adversary's plans, you wouldn't want to alter your beliefs about those plans. Conversely, if your adversary knew about your planned actions, then your adversary wouldn't want to alter their beliefs they hold about your prospective actions which underpin their planning about their future actions.

Observe this dialogue needs to happen in "real" (i.e., historical) time and not in "logical time" (in the sense of the length of a logical derivation of hypothetical dialogue). Without such actual dialogue, there's no need to come to any agreement. Scott Aaronson has shown (arXiv:cs/0406061) such dialogue can be done in finite time and, in some sense, "efficiently".

One of the problems with this, the inference of common priors from the premises on the Common Knowledge of Rationality coupled to the consistent alignment of beliefs argues the dialogue occurs in "logical time".

The problem with this is for "one shot games", where interactions between the players occur only once and in the absence of communication, there is literally no opportunity for such dialogue.

Prior Beliefs

We need some "initial beliefs" for our rational actors to have, so as to avoid an infinite regress in reciprocal expectation of actions pursued. We saw how rational actors update their beliefs via Bayesian updates, but we need some "initial prior" to start the process. Without common priors, we can get senseless results.

But the choice of prior probability distributions in Bayesian analysis can impact the posterior distribution considerably. The field of "Reference Priors" uses information theory to measure how the choice of prior distribution affects the posterior probability. The choice of priors has a rich history and while it is true "objective" (or "noninformative") priors have "minimal impact" on the posterior, but that is not the same as "zero impact". Noninformative priors can lead to improper posterior, which is dangerous. How we choose a prior seems to be a hotly contested topic (does the choice of priors "matter"? What is an appropriate way to do it?) which Andrew Gelman has written extensively on.

Even if we restrict ourselves to only "stable" priors, I'm not sure this is much progress.

Revenge of the Nerds German Philosophers

One thing which the German philosophers Kant and Hegel pondered was the self-conscious reflection of human reason upon itself. Can our reasoning faculty turn on itself and, if it can, what can it infer? Phrased more relevantly, when reason knowingly encounters itself in a game, does this tell us anything about what reason should expect of itself?

Hegel's Phenomonology of Spirit (or more generally, his philosophy of Spirit) addresses this train of thought (and more). Further Hegel takes Reason reflecting on reason as it reflects on itself as part of the restlessness which drives history. Outside of history, for Hegel, there are no answers for the question of what one's reason demands of others' reason. History provides a changing set of answers.

Also worth mentioning is that game theory uses "reason" akin to Hume's usage in his famous passage We speak not strictly and philosophically when we talk of the combat of passion and reason. Reason is, and ought only to be the slave of passions, and can never pretend to any other office than to serve and obey them. Reason is a tool to help achieve the ends of subjective passions. Hegel rejoins in his lectures on the History of Philosophy, in chapter 2 on Hume in particular, In itself reason thus has no criterion whereby the antagonism between individual desires, and between itself and the desires, may be settled. Thus everything appears in the form of an irrational existence devoid of thought; the implicitly true and right is not in thought, but in the form of an instinct, a desire.

Kant's Critique of Pure Reason via his Transcendental Dialectic investigates Reason's excesses. For other Kantian repudiations of game theoretic "reason", see O'Neil's Constructions of Reason (1989), e.g., page 27 et seq.

Conclusion

So we finally have answered the question posed so long ago: beliefs are formed by taking into account common knowledge of rationality coupled to consistent alignments of beliefs. This bootstraps a rational actor's belief system by considering that actor's rational adversary's beliefs which have already solved the riddle of what is the original actor's belief system.

And if that sounds circular...that's because it is...

References

• Shaun Hargreaves Heap and Yanis Varoufakis, Game Theory: A Critical Introduction. Second ed., Routledge. (This is the axiomatization scheme I am following.)
• John Searle, Rationality in Action. MIT Press, 2001. (This provides a different set of axioms for rational behaviour, equivalent to the axioms of game theory, and discusses implicit assumptions & its flaws.)
• S. Morris, "The Common Prior Assumption in Economic Theory". Economics and Philosophy 11 (1995) 227–253. Eprint.
• John Harsanyi, "Games with Incomplete Information Played by 'Bayesian' Players: Part 1, The Basic Model". Management Science 14, 3 (1967) 159–182. Eprint
• Robert J. Aumann, "Agreeing to Disagree" (PDF). The Annals of Statistics 4, 6 (1976) 1236–1239. doi:10.1214/aos/1176343654.
• Scott Aaronson, Common Knowledge and Aumann’s Agreement Theorem [blogpost]
• Scott Aaronson, "The Complexity of Agreement". Proceedings of ACM STOC (2005) pp. 634–643, eprint arXiv:cs/0406061

Common Knowledge of Rationality

Game theorists sought a solution to initial belief formation by treating beliefs as purely subjective assessments of a situation or matter, which could degenerate into permitting almost any belief to (and thereby action from) instrumentally rationally actors. The resolution to this was another axiom: the common knowledge of rationality.

As a rational actor, it would be prudent to stipulate your adversaries are rational actors themselves. Consequently, they would also stipulate you are rational, too. This Common Knowledge of rationality turns out to be a tacit axiom of game theory.

As an example of this, in the episode "Peak Performance" in "Start Trek: The Next Generation", the android Commander Data analyses Commander Riker's strategic abilities in a memorable scene:

DATA: I have several examples of Commander Riker's battle technique. At the Academy, he calculated a sensory blind spot on a Tholian vessel and hid within it during a battle simulation. And as a lieutenant aboard the Potemkin, his solution to a crisis was to shut down all power, and hang over a planet's magnetic poles, thus confusing his opponent's sensors.

TROI: And from these specifics, what general conclusion can you extrapolate?

DATA: Only twenty-one percent of the time does he rely upon traditional tactics. So, the Captain must be prepared for unusual cunning. Counsellor, Commander Riker will assume we have made this analysis, and knowing that we know his methods, he will alter them. But, knowing that we know that he knows that we know, he might choose to return to his usual pattern.

Data would continue in this manner ad infinitum had he not been interrupted, and it is precisely what the common knowledge of rationality states. We could formally generalize this thus:

1. each person is instrumentally rational
2. each person knows (1)
3. each person knows (2)
4. each person knows (3)
5. ...and so on ad infinitum.

How does this help? By itself, it has a fundamental problem which Heap and Varoufakis illustrate in the following example.

Suppose you have a desire to be "fashionable" when deciding what clothes to wear. But this requires taking into account that other people want to be "fashionable" too. So you need to take into account what clothes they will wear, when deciding what clothes you will wear (in order to realize your desire to be fashionable).

However, other people want to be "fashionable" too, and they will select what to wear based on the expectations of what other people (including you) will wear.

So you need to account that what clothes they will wear depends on what they think you will wear, which affects what clothes you are planning to wear. But other fashionistas, knowing this, will adjust what they wear accordingly. Knowing that you know that they know you know, you now can adjust accordingly.

And so on. This process doesn't really stop, unless we add another assumption. The belief formation doesn't "settle down" without adding an assumption about common priors, which is what Bernheim's "Rationalizable Strategic Behavior" (1984) and Pearce's "Rationalizable Strategic Behavior and the Problem of Perfection" (1984) do.

[History: D. Lewis introduced the concept of "common knowledge" when analyzing a philosophical problem in the book Conventions (1969), but Robert Aumann imported the concept to economics in his 1976 paper "Agreeing to disagree" (Annals of Statistics 4 (1976) pp. 1236–1239).]

References

• Shaun Hargreaves Heap and Yanis Varoufakis, Game Theory: A Critical Introduction. Second ed., Routledge. (This is the axiomatization scheme I am following.)
• John Searle, Rationality in Action. MIT Press, 2001. (This provides a different set of axioms for rational behaviour, equivalent to the axioms of game theory, and discusses implicit assumptions & its flaws.)
• John Geanakoplos, "Common Knowledge". Journal of Economic Perspectives 6, 4 (1992) pp. 53–82
• John Geanakoplos, "Common Knowledge". Chapter 40 in Handbook of Game Theory with Economic Applications vol 2 (eds. R.J. Aumann and S. Hart), North Holland 1994, pp. 1437–1496. SemanticScholar.
• Pierre Lescanne, "Mechanizing Common Knowledge Logic using COQ". Annals of Mathematics and Artificial Intelligence 48 1-2 (2006) pp 15–43, eprint.
• Pierre Lescanne, "Common knowledge logic in a higher order proof assistant?" arXiv:0712.3147

Criticisms of Instrumental Rationality

As a follow up to the post Agents are Instrumentally Rational, I thought it would be good to discuss a number of criticisms to instrumental rationality. It's healthy to do so, since political actors are not cold, calculating automatons. In elections, voters do not vote rationally. Politicians may or may not behave rationally. If political actors are (gasp) human, perhaps examining the flaws of rationality will illuminate aspects to better model scenarios. And unlike economists, we are trying to fit theory to reality.

There is a growing literature testing predictions "instrumental rationality" makes. Alarmingly, the vast majority of this literature finds actors are not instrumentally rational.

The basic problem seems to be, expected utility models actors as computers trying to optimize some quantity. But the human brain is more like a sophisticated "pattern recognition machine", and there are builtin "short circuits" to avoid heavy computations but tend to produce false-positives. (This is useful for doing things which do not need heavy computations; it is a feature, sometimes a bug.) This is the pioneering work of Daniel Kahneman and Amos Tversky. There is a wonderful book Thinking: Fast and Slow, by Kahneman himself, summarizing the research.

There are two points of particular concern I'll mention here. In another post, I will go on a philosophical spelunking on where this particular notion of "rationality" comes from (Hume) and the criticisms it has faced in the past.

Allais Paradox

Lets try testing the framework of preferences over prospects, specifically the independence axiom. You have to make one choice between two alternative lotteries:

Lottery 1:
Win $2500 with probability 33%
Win $2400 with probability 66%
Win nothing with 1% probability

Lottery 2: win $2400 with certainty.

Once you made that choice, you need to choose between two more lotteries:

Lottery 3:
Win $2500 with probability 33%
Win nothing with probability 67%

Lottery 4:
Win $2400 with probability 34%
Win nothing with probability 66%

Which would you prefer? What does expected utility suggest?

The expected winnings from Lottery 1 would be $2409, whereas the expected winnings from Lottery 2 is $2400. The instrumentally rational individual would pick Lottery 1, even though most people empirically choose Lottery 2.

Similarly, the expected winnings from lottery 3 is $825, whereas the expected winnings for lottery 4 is $816. But again, people choose lottery 4 over lottery 3.

The Allais Paradox is the observation that, in experiments, volunteer behavior directly contradicts rational behavior. Sugden's Rational Choice: A Survey of Contributions from Economics and Philosophy reviews the literature on this topic.

The conflict is with the axiom of independence. If we use an alternative axiomatization for rational behavior ("Savage's axioms"), the Allais paradox contradicts the "sure-thing principle".

Source of Beliefs

So, how does a rational actor "acquire" beliefs? (An instructive exercise for the reader, harking back to Socrates, is to consider how the reader "acquires" beliefs.)

For some political actors, it doesn't really matter. I'm pretty certain Senator Ted Cruz has beliefs on almost everything, and as far as how he acquired them, well, it doesn't matter.

For other types of political actors, like your "everyday voters", it does matter. Voter belief is actually a hotly debated topic: to what degree voters are "rational actors", where they acquire their party identification or how they develop affinity for a candidate, these are all hot topics.

There is universal agreement in the literature rational agents update their beliefs using Bayes inference. We should recall from probability that Bayes' theorem is a generalization of contrapositive in logic. Heuristically, what happens is we have some mathematical model of the world using random variables and parameters (denoted θ in the literature, possibly a vector of parameters). Some event E occurs, and we use adjust our model's parameters based on the event occurring.

[I don't have the space to describe the details (though I should in some future blog post), the interested reader is encouraged to read John Kruschke's Doing Bayesian Data Analysis for details.]

But where do the initial estimates for prior distributions come from? Where do the "initial beliefs" emerge? There are two answers to this query.

First answer: from the search for information itself. People do not sit around waiting for "information" to fall into their laps. No! Rational actors must actively pursue information. The original "prejudices" (initial beliefs) are adjusted as more information is actively obtained.

When does a rational actor cease seeking information? Economists answer, with either a sigh or a smile, the rational actor will stop when the utility of the information gained equals the cost of the search for that information (with the cost evaluated in utility terms). As long as there is more utility gleaned from seeking than it costs to seek, a rational actor will keep searching. This is a rather cute, self-consistent solution.

But it begs the question: how does an actor know how to evaluate the utility of the new information prior to obtaining it? Perhaps our actor has formulated expectations about the value of additional information. How did our actor acquire that expectation of the value of information?

A waggish defender might say, "By acquiring information about the value of information up to the point where the marginal benefits of this (second-order) information were equal to the costs." This solution really degenerates into an infinite regress, since we can ask the same question of how the actor knows value of this second-order information.

There are two ways to stop the infinite regress:

1. Something additional is needed. This concedes the instrumental rationality paradigm is incomplete.
2. The only alternate would be to assume that the individual knows the benefits the actor can expect from a little more search because the actor knows the full information set. But then there is no problem: the actor knows everything already!

I wonder if we might not be more generous with the waggish defender, and try to bootstrap some interpolated polynomial from first-order, second-order, ..., N-order costs of information? My intuition suggests the answer to be "In general, no; only for a few special edge cases can this bootstrap occur coherently."

A last remark: this discussion reminds me of Meno's paradox (not to be confused with Zeno's paradox). In Plato's dialogue, Meno, Meno asks Socrates And how will you inquire into a thing when you are wholly ignorant of what it is? Even if you happen to bump right into it, how will you know it is the thing you didn't know? [80d1-4] Socrates reformulates it thus [A] man cannot search either for what he knows or for what he does not know[.] He cannot search for what he knows—since he knows it, there is no need to search—nor for what he does not know, for he does not know what to look for. [80e] Or, phrased more relevantly for our discussion, how can a rational actor actively pursue information about a matter which the actor is completely ignorant of?

I'm sure the rejoinder would be, "Rational actors seek information precisely how Socrates sought answers to questions on matters he professed ignorance about." But it still dodges the question.

Second answer: Beliefs as purely subjective assessments. This is following Savage's The foundations of statistics (1954), where beliefs are purely subjective assessments. They are what they are, and only revealed ex post by the choices people make.

This avoids a lot of the problems plaguing the first answer. Unfortunately, we have some experimental evidence casting doubt on the consistency of such subjective assessments and more generally on the probabilistic representations of uncertainty; most famous of which is the Ellsberg paradox.

Game theory has been pursuing the line of reasoning Savage provides. But then this may license any kind of action, rendering instrumental rationality nearly vacuous. Game theorists have sought to prevent this "purely subjective assessments" turning against itself [i.e., letting "anything" be a solution to describe rational behavior] by supplementing instrumental rationality with the assumption of the common knowledge of rationality. This leads to weak solutions to game theoretic problems apparently called Rationalizability, not to be confused with the psychological mechanism of "Rationalizing" (i.e., lying to one's self to feel better).

References

• Shaun Hargreaves Heap and Yanis Varoufakis, Game Theory: A Critical Introduction. Second ed., Routledge.
• John Searle, Rationality in Action. MIT Press, 2001.

Savage Axioms

• L. J. Savage, The foundations of statistics. John Wiley & Sons Inc., New York (1954).
• Judea Pearl, The Sure-Thing Principle. UCLA Cognitive Systems Laboratory, Technical Report R-466 (2016).
• Dov Samet, "The sure-thing principle and independence of irrelevant knowledge". Israel Institute of Business Research, 2008.
• Edi Karni, Savages’ Subjective Expected Utility Model. Lecture notes, 2005.

Animals and Rational Behaviour

Having introduced a notion of Instrumental Rationality, perhaps a good question to ask is "What is an example of a rational agent which is not human?"

It might seem that animals behave rationally at times; for example, worker bees give up their own production in favor of other offspring of the queen, surely this must give some benefit to the donor. This idea (generalizing the bee situation) is known as Hamilton's Rule, and it doesn't really work. For example, it is neither testable nor does it make predictions.

With the bees, the altruist (i.e., worker bee) cooperates by giving a benefit b to the recipient (another offspring) at a cost c to itself. Both b and c are measured in terms of fitness, specifically the expected number of offspring. Naively one might expect b > c to suffice, but Hamilton's major insight was that relatedness ("degree of kinship") r between donor and recipient must enter into the equation, giving us Hamilton's rule br > c.

Game theorists are overjoyed to hear this can be derived from utility maximization, and one might expect it to have a status similar to Newton's laws in physics. However, Nowak, Tarnita, and Wilson have argued that Hamilton's rule almost never holds. In short, simple game theoretic models here fail to describe the biological situation.

Decades ago, evolutionary biologists would have treated Hamilton's rule as an "iron law". That no longer seems to be the case. For more on this, see de Vladar and Szathmáry's "Beyond Hamilton's Rule".

Agents are Instrumentally Rational

Game Plan: We'll introduce the notion of "instrumental rationality" as an ordering of alternatives with some technical condition. Then we'll discuss measures of "preference" via utility functions. Then we conclude by discussing maximizing utility under uncertainty.

Loosely put, individuals who are instrumentally rational have preferences over various "things" (e.g., baby-back ribs are preferred to chicken, and chicken is preferred to bread). Such individuals are deemed "rational" for picking actions which satisfy those preferences. The only constraint is that preferences are ordered in some suitably "weakly coherent" way (e.g., ribs are still preferred to bread if there is no chicken).

The convention is to call these "things" preferred as "Alternatives".

Definition 1. Let an actor be choosing between countably many possible different alternatives x₁, x₂, x₃, …. An actor is called Instrumentally Rational if the actor has preferences satisfying the following conditions:

1. Reflexivity: No alternative x_i is less preferred than itself.
2. Completeness: For any two alternatives x_i and x_j, either (1) x_i is strictly preferred over x_j, (2) x_j is strictly preferred over x_i, or (3) the actor is indifferent between the two alternatives.
3. Transitivity: For any alternatives x_i, x_j, x_k, if x_i is no less desired than x_j, and if x_j is no less desired than x_k, then x_i is no less desired than x_k.
4. Continuity: For any alternatives x_i, x_j, x_k, if x_i is (strictly) preferred to x_j, and if x_j is (strictly) preferred to x_k, then there exists some "composite" of x_i and x_k (call it y) which is equally as desired as x_j.

Remark 1 (On Continuity). There are two ways to interpret the continuity axiom. The first perspective is to think of y as a "basket" containing "bits" of x_i and "bits" of x_k. For example, if x_i is "18 ribs", x_j is "half a roasted chicken", and x_k is "10 rolls", then there is some composite ("9 ribs and 5 rolls") which is equally as desirable as half a chicken.

The other perspective is to think of y as a lottery, where the actor obtains x_i with probability p (0 < p < 1) and x_k with probability 1 − p. The continuity axiom then says there is some p for which the actor is indifferent between the lottery y and the alternative x_j.

Remark 2 (Ordering, Utility Functions). The first three axioms taken together implies the actor has a well-defined preference ordering (in the mathematical sense). When the continuity axiom is added, the preference ordering may be "represented" by a utility function (i.e., a function assigning to each alternative x_i some real number U(x_i) reflecting the "utility" or "desire" for that alternative). An actor making choices to satisfy his or her preference ordering can be viewed "as if" maximizing his or her utility function.

Now, discussions of "utility" of an alternative should not be confused with the philosophy of Utilitarianism. A utility function just assigns some numbers such that the ordering induced by it is the same as the actor's preference relation. That is to say, U(x_i) > U(x_j) if and only if x_i is strictly preferred to x_j. The numbers represented by U(x_i) are measured in utils, which is Agent-dependent and measures that Agent's preference for the given alternative.

Ordinal Utilities, Cardinal Utilities, Maximizing Expected Utility

Definition 2. If we assign utility "arbitrarily" but in a manner consistent with the preference ordering (e.g., for any alternatives X and Y such that X is preferred to Y, we assign the utilities such that U(X) > U(Y) but otherwise the quantities remain arbitrary), then we call such utility the Ordinal Utility.

Here we must stress again there are two important points of assigning utility in a manner which captures only the preference ordering (and nothing else).

First, ordinal utility does not describe the agent's "intensity of desire" for an alternative. The "strength of preference" is not captured by this notion. So how much more I want ribs than chicken is not adequately described by this notion, just the fact that I really want ribs right now (and not chicken, much less bread).

Second, ordinal utility cannot be compared "across agents". The ordinal utility I assign to a full rack of baby-back ribs cannot be compared to anyone else's ordinal utility for, say, Lasagna. We can only compare my ordinal utility for baby-back ribs against my ordinal utility for Lasagna.

Dealing with Uncertainty

My local BBQ joint smokes 1 pig per day, and when it's all sold, there's no more. If I am hungry, should I go before the lunch rush or afterwards?

Here we must talk of Prospects, outcomes and their associated probabilities.

For our particular situation, there is a decision I must make (go before the lunch rush or after) and two outcomes (there is food left, or they ran out of food). One prospect is given by the possible outcomes to a given choice of going before the lunch rush (go before lunch AND they have food, go before lunch AND no more food; p, 1 − p). The other prospect is given by the decision to go after the lunch rush (go after lunch AND they have food, go after lunch AND no more food; q, 1 − q).

Observe, each decision has different possible outcomes, but the probabilities for the outcomes on a given decision must sum to 100%: something must happen when I take a decision.

We now need to consider preference ordering over prospects.

Definition 3. Suppose a person must choose between actions with uncertain outcomes, in the sense that: each action has various possible outcomes associated with it, each with some probability. We call this action a Prospect and represent it by a pairing of the possible outcomes with their respective probabilities (y₁, y₂, ...; p₁, p₂, ...) where the outcome y_i occurs with probability p_i, and the probabilities sum to 1 = p₁ + p₂ + ... (since there must be an outcome to the action).

Remark. There is a "nested structure" to prospects, in the sense that y_i might be an "atomic outcome" (e.g., "there will be food", "there will be no food", "it will rain", "the world will end", etc.) or another prospect (imagine "I flip a coin; if it is heads, then I do this action, but if it is tails then I do some other action").

An actor's Preferences over Prospects are called Consistent if the preference satisfies axioms (1), (2), and (3) of Definition 1, and:

4. Continuity: Consider three prospects y_i, y_j, and y_k, and suppose the first is preferred to the second and the second is preferred to the third. Then there exists some probability p such that the prospect (y_i, y_k; p, 1 − p) is equally as preferable to y_j (compare to the second interpretation forwarded in Remark 1).
5. Preference increasing with probability: If y_i is preferred to y_j, letting y_m = (y_i, y_j; p₁, 1 − p₁) and y_n = (y_i, y_j; p₂, 1 − p₂), then y_m is preferred to y_n only if p₁ > p₂.
6. Independence: For any three prospects y_i, y_j, and y_k, if y_i is preferred to y_j, then there exists a probability p such that the prospect (y_i, y_j; p, 1 − p) is no less desired than (y_i, y_k; p, 1 − p)

Given this notion of "consistent preferences over uncertain prospects", how can we develop a notion of instrumental rationality?

Maximizing Expected Utility

The first step is to introduce the notion of Cardinal Utility, which assigns to a given outcome y_i the intensity for an agent's preference for that outcome u(y_i).

The second step is to consider the Expected Utility of a Prospect y = (y₁, y₂, ...; p₁, p₂, ...) as the sum E_u[y] = u(y₁)p₁ + u(y₂)p₂ + ..., which is the expected value of the "random variable".

Now, an agent with cardinal utility u(-) is considered instrumentally rational if it picks the action whose prospect has the maximum expected utility.

Example 1. If I go to my favorite BBQ restaurant before the lunch rush, the prospect looks like ("get food", "no food"; 0.95, 0.05). If I leave after the lunch rush, the prospect looks like ("get food", "no food"; 0.1, 0.9).

My cardinal utility function looks like u(get food) = 10, u(no food) = −30.

The expected utility for going before the lunch rush is then

E[before]	=	u(get food)×0.95 + u(no food)×0.05
	=	10×0.95 − 30×0.05
	=	9.5 − 1.5
	=	8

The expected utility for going after the lunch rush is then

E[after]	=	u(get food)×0.1 + u(no food)×0.9
	=	10×0.1 − 30×0.9
	=	1 − 27
	=	−26

Since 8 > −26, it is rational to go before the lunch rush to try to get food.

Next time, we'll discuss flaws with this notion of instrumental rationality, both logical and empirical.

References

• Shaun Hargreaves Heap and Yanis Varoufakis, Game Theory: A Critical Introduction. Second ed., Routledge. (This is the axiomatization scheme I am following.)
• John Searle, Rationality in Action. MIT Press, 2001. (This provides a different set of axioms for rational behaviour, equivalent to the axioms of game theory, and discusses implicit assumptions & its flaws.)