The Ellsberg Paradox

According to Smithsonian Magazine

Ellsberg reprised the story of how he became, as Henry Kissinger once put it, “the most dangerous man in America.”

During the mid-1960s, Ellsberg, a former Marine Corps officer with a PhD in economics from Harvard, was in Vietnam, working for the U.S. State Department, getting a first-hand look at the war.

He saw villages that had been burned because Viet Cong had slept there for a night.

He returned to the U.S. in 1967, convinced that the military strategy was doomed to fail and increasingly disenchanted with the war.

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Once back home, Ellsberg worked as a military analyst at the Rand Corporation, a consulting firm based in Santa Monica.

He had access to a 7,000-page Pentagon report on the war’s history and progress (or lack thereof), kept in a safe in his office.

Only he and Harry Rowen, the head of Rand, were authorized to read it.

What would come to be known as the Pentagon Papers, was so restricted, it wasn’t included on Rand’s list of classified documents.

Daniel Ellsberg and the Pentagon Papers  Daniel Ellsberg was an employee of the Defense ...

“When routine inventories of the contents of safes were done,”

he recalls, “I had to take all 47 volumes to Rowen’s office in a grocery cart.”

Distressed by what the report revealed, in 1969 Ellsberg began taking pages out of the office at night and photocopying them at an advertising agency run by a friend.

Helped by Rand colleague Anthony Russo, he continued into 1970, then gave copies to certain members of Congress and to New York Times reporter Neil Sheehan.

Despite agreeing to keep the report under wraps, Sheehan and editor Gerald Gold began excerpting the report in the newspaper on June 13, 1971.

The White House Plumbers  After the release of the ...

The front- page revelations of continued deceptions gave powerful impetus to the anti-war movement and infuriated President Richard Nixon.

Later that year, Ellsberg and Russo were charged under the Espionage Act of 1917.Their trial began early in 1972.

Ellsberg faced a possible sentence of 115 years.

“I was the first person ever indicted for a leak of classified information,” he said.

“I was prepared to go to prison.

The Watergate Break-in  When initial polls showed Nixon in the Election of 1972, ...

The creation of the plumbers, however, was never about the Pentagon Papers.

Nixon considered all that history, about the Kennedy and Johnson years.

But I had worked for Henry Kissinger in 1969 at the National Security Council, so I knew about Nixon’s big plan for expanding the war, including use of tactical nuclear weapons.

Nixon didn’t know how much I knew, but he feared the worst.”

On an Oval Office tape, from July 27, 1971, Kissinger, speaking to Nixon, referred to Ellsberg as “that son of a bitch….I would expect—I know him well…I am sure he has some more information.”

Woodward, Bernstein and the Washington Post Watergate came to public attention largely through the work of Bo...

A short time later, Hunt drafted a proposal

to “neutralize Ellsberg,” leading to the Fielding operation.

The break-in was revealed only after a nine-month recess in the trial, calculated by the White House to keep Ellsberg off the witness stand and out of the news, until after the presidential election.

“The first time I found out about the break-in,” Ellsberg said, “was when government prosecutors revealed it to the judge, and he told my lawyers.

Nixon had wanted that information withheld, but he’d been warned that this could make him criminally liable.

The judge cited government misconduct and dismissed all charges.”

Watergate Enters the Nixon Campaign  The break-in was eventually tied to the Nixon r...

News reports at the time claimed that the burglars hadn’t located Ellsberg’s file.

“The plumbers did find my file,” Ellsberg told me.

“In it was a paper I had written for the American Political Science Association called ‘Quagmire Myth and the Stalemate Machine.’ I alluded to classified information I’d seen, which obviously meant the Pentagon report.”

The Watergate Investigations: Judge John Sirica  Watergate came to be investigated by...

At a neighborhood restaurant, where we drove in Ellsberg’s slightly beat-up red Miata, he speculated on the ironies of history.

“Had my lawyers and I known about the break-in from the beginning, [John] Ehrlichman would have had to shut down the illegal plumbers operation, and the Watergate break-in of June 1972 might never have taken place.

Daniel Ellsberg graffiti. The filing cabinet from the office of Dr. Lewis Fielding which was broken into by E. Howard Hunt, G. Gordon Liddy, Eugenio Martinez, Felipe de Diego, and Bernard Barker on September 3, 1971. Photo credit: thierry ehrmann / Flickr (CC BY 2.0) and Tim Evanson / Flickr (CC BY-SA 2.0)

”NMAH curator Harry Rubenstein concurs. “Would the plumbers group have been formed if they hadn’t wanted Ellsberg’s file?

Probably not.” This humble filing cabinet, he says, “was the beginning of the end of the Nixon presidency.”

Senate Investigation and the Oval Office Tapes  The Senate began hearings into Watergat...

Ellsberg began working as a strategic analyst at the RAND Corporation for the summer of 1958 and then permanently in 1958.

 He concentrated on nuclear strategy and the command and control of nuclear weapons.

 Nuclear strategy involves the development of doctrines and strategies for the production and use of nuclear weapons.

As a sub-branch of military strategy, nuclear strategy attempts to match nuclear weapons as means to political ends.

In addition to the actual use of nuclear weapons whether in the battlefield or strategically, a large part of nuclear strategy involves their use as a bargaining tool.

Some of the issues considered within nuclear strategy include:

  • Under what conditions does it serve a nation’s interest to develop nuclear weapons?
  • What types of nuclear weapons should be developed?
  • When and how should such weapons be used?

Many strategists argue that nuclear strategy differs from other forms of military strategy. The immense and terrifying power of the weapons makes their use, in seeking victory in a traditional military sense, impossible.

Perhaps counterintuitively, an important focus of nuclear strategy has been determining how to prevent and deter their use, a crucial part of mutual assured destruction.

In the context of nuclear proliferation and maintaining the balance of power, states also seek to prevent other states from acquiring nuclear weapons as part of nuclear strategy.

Ellsberg completed a PhD in Economics from Harvard in 1962.

His dissertation on decision theory was based on a set of thought experiments that showed that decisions under conditions of uncertainty or ambiguity generally may not be consistent with well defined subjective probabilities.

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Now known as the Ellsberg paradox, this formed the basis of a large literature that has developed since the 1980s, including approaches such as Choquet expected utility and info-gap decision theory.

The basic idea is that people overwhelmingly prefer taking on risk in situations where they know specific odds, rather than an alternative risk scenario, in which the odds are completely ambiguous

they will always choose a known probability of winning over an unknown probability of winning

even if the known probability is low and the unknown probability could be a guarantee of winning.

That is, given a choice of risks to take (such as bets), people “prefer the devil they know” rather than assuming a risk where odds are difficult or impossible to calculate.

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Ellsberg actually proposed two separate thought experiments, the proposed choices in which contradict subjective expected utility.

The 2-color problem involves bets on two urns, both of which contain balls of two different colors.

The 3-color problem, described below, involves bets on a single urn, which contains balls of three different colors.

An example was posted in Neuroeconomics: The Consilience of Brain and Decision

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In Ellsberg’s (1961) paradox you are presented with an urn, and you are told that it contains 90 balls.

Of these, 30 are blue, and 60 are either red or yellow; any proportion is possible.

You are then offered a choice between, a lottery that pays $100, if a blue ball is drawn (a 1/3 probability) and one that pays $100, if a red ball is drawn.

The probability of a red draw is unspecified or ambiguous:

It is a choice between an event with a known probability and an event with an unknown probability. Under these circumstances, people typically choose the first lottery, which wins if a blue ball is drawn.

According to expected utility theory they could only do so if they believe that there are fewer than 30 red balls in the urn or, equivalently, that there are more than 30 yellow balls.

Then (before any balls are actually drawn, but with the same urn standing in front of you) you are asked to choose again, this time between a lottery that pays $100 on either blue or yellow and one that pays $100 on either red or yellow.

Now the likelihood of winning is clear in the second case (a 2/3 probability of winning $100) but unclear in the first case (a probability between 1/3 and 1).

People this time typically choose the second lottery. The first lottery seems less attractive, because there might be too few yellow balls.

Is there anything wrong with this behavior?

If expected utility theory is correct, then there certainly is: You cannot think that there are too few and too many yellow balls in the urn at the same time.

The Ellsberg paradox is just one of many demonstrations presented in the last half of the twentieth century,  considered formal falsifications of expected utility theory.

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An even earlier example is Allais’ paradox , based on the idea that a certain outcome may be perceived as more desirable, in a qualitatively different way, than any random outcome, even if very likely .

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These examples proved that expected utility theory as originally proposed could not be globally correct; at best it could only predict choices under some circumstances.

This has led economists and social psychologists both to attempt modifications to expected utility theory and to replace it outright.

Both the modifications and replacements have provided important and economically powerful insights into choice behavior

but have not yet provided a global theory of choice that can truly replace expected utility theory.

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The emerging discipline of neuroeconomics offers a new strategy both for testing existing models of all types and for developing new models with empirical techniques.

If we succeed in understanding mechanistically how choices that violate expected utility theory are made at a neural level, then a new global theory of choice will be developed.

To that end, a number of laboratories are now beginning to reexamine the conditions under which expected utility theory fails.

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The reason that expected utility theory fails under some conditions may be that choosers use more than one evaluative mechanism at a neurobiological level

(. For example, in Dickhaut et al. , the processes involved when a certain outcome is one of the options are different

from those involved when only random outcomes are at stake, providing an explanation of the Allais’ paradox cited above.

Under many conditions these mechanisms may work together to yield choices similar to those predicted by expected utility theory but may produce odd results when used in isolation, in novel combinations, or in situations for which they are ill suited.

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Neuroeconomics is an interdisciplinary field that seeks to explain human decision making, the ability to process multiple alternatives and to follow a course of action.

Recent work by Damasio and colleagues [for example, ] on the class of behavioral paradoxes from which the Ellsberg example is drawn seem to support this conclusion.

These studies suggest that an ambiguity-sensitive mechanism associated with the expression of emotion may reside, at least in part, in the ventromedial prefrontal cortex (VMPFC) (Fig. 4) and may be responsible for choice under some but not all conditions.

These researchers and others have shown that patients with damage to this area have an impaired ability to make some classes of decisions and have difficulties planning their work and choosing friends.

Further, the actions these individuals do elect to pursue often lead to financial as well as personal losses.

 

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Yet despite these specific failures, patients with damage to the VMPFC show normal performance on multiple-choice tests of intelligence.

Medial view of the left half of a human brain, with the front of the brain on the right side of the image.

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The human ventro medial prefrontal cortex is shown in red.

These observations and others like them have led Damasio to propose that the inability of patients with VMPFC lesions to make advantageous decision sunder some circumstances is caused by damage to an emotional mechanism that stores and signals the value of future consequences of an action,

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the somatic marker hypothesis.

The hypothesis proposes that, because they lack this emotional mechanism, the patients must rely on other brain mechanisms that achieve a different analysis of the numerous and often conflicting options involving both immediate and future consequences.

This other mechanism, operating alone, is hypothesized to produce decisions that are less efficient and slower than those produced by a normal, intact, system.

The importance of the emotion-related VMPFC for regular decision-making has been confirmed by experiments where subjects were asked to make choices among a group of alternatives that carry a monetary reward (typically by selecting one card at a time from four different decks of cards),but for which the probability of reward is unspecified .

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This is precisely the ambiguous situation that produces Ellsberg’s paradox.

Under these conditions, patients with VMPFC lesions seem to lack an aversion to ambiguity or losses that normal subjects have, an aversion that may be quite advantageous under many conditions.

Further support for this hypothesis comes from brain imaging studies.

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For example, O’Doherty et al.  have shown that the VMPFC is relatively more active when human subjects are actively learning

about the availability of rewards and punishments during one of these ambiguous choice tasks.

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Dopamine is also what makes people addicted to learning or information

The process may be very different, however, when subjects simply choose between options without any feedback or learning taking place at the same time.

For example, Rustichini et al. asked normal subjects to make choices among ambiguous lotteries,

risky lotteries, and certain outcomes while their brain activity was monitored.

Subjects were paid for the outcome of their choices, but the outcome was communicated only after the experiment was over.

Under these conditions, the VMPFC did not show any activation; it was actually less active when choices were being made than when subjects waited between trials.

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These results suggest that emotional circuits may be important in learning and processing information, rather than in selecting among alternatives.

Together, these data may begin to explain, in a mechanistic way, how information is analyzed when at least one class of behavior

which is not predicted by the expected utility theory is produced.

The process of learning and evaluating feedback may involve emotion-related areas.

Ambiguity aversion, whether advantageous or disadvantageous in a particular situation,

may become explicable as we learn more about the computations that brain areas like the VMPFC perform.

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decision theory and economics, ambiguity aversion (also known as uncertainty aversion) is a preference for known risks over unknown risks. An ambiguity-averse individual would rather choose an alternative where the probability distribution of the outcomes is known over one where the probabilities are unknown.

Strategic cooperation. As with the Ellsberg paradox, challenges have also been raised recently to classical game theory.

In a path-breaking study, Guth et al.  analyzed the behavior of subjects playing the ultimatum game.

In this game, a first player, the proposer, has $10 to split with a second player.

He can offer any amount between zero and $10.

The second player is informed of the offer and can accept or refuse. If she accepts, the split is made.

If she refuses, both players get nothing.

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The prediction of a restrictive concept of game theory, the sub game perfect equilibrium, is that for any positive amount offered by the proposer,

the second player knows that she faces a choice between gaining nothing (if she refuses the offer) or something (if she accepts).

The proposer should therefore always offer the minimum possible split to player two, who should always accept.

Contrary to this prediction, the robust experimental finding is that low offers (typically $2 or even $3) are consistently refused.

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The second player appears to prefer, under these conditions, to gain nothing. Anticipating this, proposers typically avoid low offers.

Although expected utility theorists have proposed some explanations for this behavior,

it may well be that by analyzing the neural circuits active during the ultimatum game we may be able to both explain the causes of this behavior and to predict it.

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Studying the ultimatum game in subjects undergoing brain scans,

Sanfey et al.  found that offers refused by the second players activated specific brain circuits in those players, and interestingly these brain circuits are also associated with emotional arousal:

the anterior insula (AI, associated with disgust, both physical and emotional), the dorsolateral prefrontal cortex (DLPFC, associated with goal maintenance

and executive control), and the anterior cingulate cortex (ACC, associated with detection of cognitive conflict).

Also significant is the correlation of activation with choices:

An activation of the AI is positively correlated with rejection, suggesting that an emotional arousal associated with a low offer is correlated with rejection.

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The overall picture is that offers we might consider unfair may activate emotional circuits of the brain involved in the decision to reject an offer.

If we can come to more fully understand how these circuits reach this conclusion, then a behavior that was difficult for classical game theory to predict may become fully explicable with the synthetic approach that neuro economics provides.

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A similar line of investigation has examined inter player cooperation during single rounds of the trust game. In this game, two players move sequentially.

The first player can decide to transfer a sum of money out of an initial endowment that she receives into an investment pool that immediately triples in value.

The second player then gains control of the investment and can divide it between the two players in any way he chooses.

In this game, the only Nash equilibrium choice for the first player is to transfer nothing into the investment.

Were she to make any transfer, the second player should take all of the money for himself.

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However, in real experiments the first player typically does transfer a significant amount into the investment, and the second player reciprocates by returning part of the pool.

McCabe et al. (had subjects play the trust game both against a human opponent and against a computer program which, they were told, would play a human-like strategy.

Under these conditions McCabe and colleagues found that subjects were more likely to cooperate with real humans than with computers and that cooperators have a significantly different brain activation in the two conditions.

Cooperation is associated with activation of the anterior paracingulate cortex, a brain region associated with  interpreting and monitoring the mental state of others.

Although these studies are in their early stages, they suggest the existence of specific brain components that make specialized contributions to decision making.

The challenge that these studies face is to derive detailed computational models of the neural mechanisms, which will make neuroeconomic models broadly predictive as well as explanatory.

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Plumbers LSD 

Bizarrely , Ellsberg later claimed that after his trial ended, Watergate prosecutor William H. Merrill informed him of an aborted plot by Liddy

and the “Plumbers” to have 12 Cuban Americans who had previously worked for the CIA “totally incapacitate” Ellsberg, when he appeared at a public rally.

It is unclear, whether they were meant to assassinate Ellsberg or merely to hospitalize him.

 In his autobiography, Liddy describes an “Ellsberg neutralization proposal”

originating from Howard Hunt, which involved drugging Ellsberg with LSD, by dissolving it in his soup, at a fund-raising dinner in Washington in order to “have Ellsberg incoherent by the time he was to speak” and thus ” make him appear a near burnt-out drug case” and “discredit him.”

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LSD is a potent and illegal hallucinogen that blurs the line between perception and imagination. Use may trigger the onset of schizophrenia in those predisposed to the condition. 

The plot involved waiters from the Miami Cuban community. According to Liddy, when the plan was finally approved,

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“there was no longer enough lead time to get the Cuban waiters up from their Miami hotels and into place in the Washington Hotel where the dinner was to take place”

and the plan was “put into abeyance pending another opportunity.”

The Doomsday Machine

In December 2017, Ellsberg published The Doomsday Machine: Confessions of a Nuclear War Planner, a book with his recollections and analysis of a second cache of secret documents related to the U.S. nuclear arsenal.

The book stated that US governments documents revealed that President Eisenhower empowered a few top military officers to be able to use nuclear weapons

without presidential authorization or no way to contact the president.

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Ellsberg believes that similar procedures remain in place today – in sharp contrast to what the American public is told about how the “nuclear football” works.

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In the book, Ellsberg revealed that he had made copies of sensitive U.S. nuclear planning materials and memos

he had reviewed during his time at the RAND Corporation,

and intended to leak them to the public shortly after the Pentagon Papers were published.

However, during the time of Ellsberg’s trial, these nuclear planning materials were hidden in a briefcase buried in a landfill, and were lost when an unexpected tropical storm descended on the region

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