How Not to Be Wrong : The Power of Mathematical Thinking (9780698163843)
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“The most plausible reading of this data is that the public wants a free lunch,” economist Bryan Caplan wrote. “They hope to spend less on government without touching any of its main functions.” Nobel Prize−winning economist Paul Krugman: “People want spending cut, but are opposed to cuts in anything except foreign aid. . . . The conclusion is inescapable: Republicans have a mandate to repeal the laws of arithmetic.” The summary of a February 2011 Harris poll on the budget describes the self-negating public attitude toward the budget more colorfully: “Many people seem to want to cut down the forest but to keep the trees.” It’s an unflattering portrait of the American public. Either we are babies, unable to grasp that budget cuts will inevitably reduce funding to programs we support; or we are mulish, irrational children, who understand the math but refuse to accept it.
How are you supposed to know what the public wants when the public makes no sense?
RATIONAL PEOPLE, IRRATIONAL COUNTRIES
Let me stick up for the American people on this one, with the help of a word problem.
Suppose a third of the electorate thinks we should address the deficit by raising taxes without cutting spending; another third thinks we should cut defense spending; and the rest think we should drastically cut Medicare benefits.
Two out of three people want to cut spending; so in a poll that asks “Should we cut spending or raise taxes?” the cutters are going to win by a massive 67−33 margin.
So what to cut? If you ask, “Should we cut the defense budget?” you’ll get a resounding no: two-thirds of voters—the tax raisers joined by the Medicare cutters—want defense to keep its budget. And “Should we cut Medicare?” loses by the same amount.
That’s the familiar self-contradicting position we see in polls: We want to cut! But we also want each program to keep all its funding! How did we get to this impasse? Not because the voters are stupid or delusional. Each voter has a perfectly rational, coherent political stance. But in the aggregate, their position is nonsensical.
When you dig past the front-line numbers of the budget polls, you see that the word problem isn’t so far from the truth. Only 47% of Americans believed balancing the budget would require cutting programs that helped people like them. Just 38% agreed that there were worthwhile programs that would need to be cut. In other words: the infantile “average American,” who wants to cut spending but demands to keep every single program, doesn’t exist. The average American thinks there are plenty of non-worthwhile federal programs that are wasting our money and is ready and willing to put them on the chopping block to make ends meet. The problem is, there’s no consensus on which programs are the worthless ones. In large part, that’s because most Americans think the programs that benefit them personally are the ones that must, at all costs, be preserved. (I didn’t say we weren’t selfish, I just said we weren’t stupid!)
The “majority rules” system is simple and elegant and feels fair, but it’s at its best when deciding between just two options. Any more than two, and contradictions start to seep into the majority’s preferences. As I write this, Americans are sharply divided over President Obama’s signature domestic policy accomplishment, the Affordable Care Act. In an October 2010 poll of likely voters, 52% of respondents said they opposed the law, while only 41% supported it. Bad news for Obama? Not once you break down the numbers. Outright repeal of health care reform was favored by 37%, with another 10% saying the law should be weakened; but 15% preferred to leave it as is, and 36% said the ACA should be expanded to change the current health care system more than it currently does. That suggests that many of the law’s opponents are to Obama’s left, not his right. There are (at least) three choices here: leave the health care law alone, kill it, or make it stronger. And each of the three choices is opposed by most Americans.*
The incoherence of the majority creates plentiful opportunities to mislead. Here’s how Fox News might report the poll results above:
Majority of Americans oppose Obamacare!
And this is how it might look on MSNBC:
Majority of Americans want to preserve or strengthen Obamacare!
These two headlines tell very different stories about public opinion. Annoyingly enough, both are true.
But both are incomplete. The poll watcher who aspires not to be wrong has to test each of the poll’s options, to see whether it might break down into different-colored pieces. Fifty-six percent of the population disapproves of President Obama’s policy in the Middle East? That impressive figure might include people from both the no-blood-for-oil left and the nuke-’em-all right, with a few Pat Buchananists and devoted libertarians in the mix. By itself, it tells us just about nothing about what the people really want.
Elections might seem an easier case. A pollster presents you with a simple binary choice, the same one you’ll face at the ballot box: candidate 1, or candidate 2?
But sometimes there are more than two. In the 1992 presidential election, Bill Clinton drew 43% of the popular vote, ahead of George H. W. Bush with 38% and H. Ross Perot at 19%. To put it another way: a majority of voters (57%) thought Bill Clinton shouldn’t be president. And a majority of voters (62%) thought George Bush shouldn’t be president. And a really big majority of voters (81%) thought Ross Perot shouldn’t be president. Not all those majorities can be satisfied at once; one of the majorities won’t get to rule.
That doesn’t seem like such a terrible problem—you can always award the presidency to the candidate with the highest vote tally, which, apart from Electoral College issues, is what the American electoral system does.
But suppose the 19% of voters who went with Perot broke down into 13% who thought Bush was the second-best choice and Clinton the worst of the bunch,* and 6% who thought Clinton was the better of the two major-party candidates. Then if you asked voters directly whether they preferred to have Bush or Clinton as president, 51%, a majority, would pick Bush. In that case, do you still think the public wants Clinton in the White House? Or is Bush, who most people preferred to Clinton, the people’s choice? Why should the electorate’s feelings about H. Ross Perot affect whether Bush or Clinton gets to be president?
I think the right answer is that there are no answers. Public opinion doesn’t exist. More precisely, it exists sometimes, concerning matters about which there’s a clear majority view. Safe to say it’s the public’s opinion that terrorism is bad and The Big Bang Theory is a great show. But cutting the deficit is a different story. The majority preferences don’t meld into a definitive stance.
If there’s no such thing as the public opinion, what’s an elected official to do? The simplest answer: when there’s no coherent message from the people, do whatever you want. As we’ve seen, simple logic demands that you’ll sometimes be acting contrary to the will of the majority. If you’re a mediocre politician, this is where you point out that the polling data contradicts itself. If you’re a good politician, this is where you say, “I was elected to lead—not to watch the polls.”
And if you’re a master politician, you figure out ways to turn the incoherence of public opinion to your advantage. In that February 2011 Pew poll, only 31% of respondents supported decreasing spending on transportation, and another 31% supported cutting funding for schools; but only 41% supported a tax hike on local businesses to pay for it all. In other words, each of the main options for cutting the state’s deficit was opposed by a majority of voters. Which choice should the governor pick to minimize the political cost? The answer: don’t pick one, pick two. The speech goes like this:
“I pledge not to raise taxes a single cent. I will give municipalities the tools they need to deliver top-quality public services at less cost to the taxpayers.”
Now each locality, supplied with less revenue by the state, has to decide on its own between the remaining two options: cut roads or cut schools. See the genius here? The governor has specifically excluded raising taxes, the most popula
r of the three options, yet his firm stand has majority support: 59% of voters agree with the governor that taxes shouldn’t rise. Pity the mayor or county executive who has to swing the axe. That poor sap has no choice but to execute a policy most voters won’t like, and suffers the consequence while the governor sits pretty. In the budget game, as in so many others, playing first can be a big advantage.
VILLAINS OFTEN DESERVE WHIPPING, AND PERHAPS HAVING THEIR EARS CUT OFF
Is it wrong to execute mentally retarded prisoners? That sounds like an abstract ethical question, but it was a critical issue in a major Supreme Court case. More precisely, the question wasn’t “Is it wrong to execute mentally retarded prisoners?” but “Do Americans believe it’s wrong to execute mentally retarded prisoners?” That’s a question about public opinion, not ethics—and as we’ve already seen, all but the very simplest questions about public opinion are lousy with paradox and confusion.
This one is not among the very simplest.
The justices encountered this question in the 2002 case Atkins v. Virginia. Daryl Renard Atkins and a confederate, William Jones, had robbed a man at gunpoint, kidnapped him, and then killed him. Each man testified that the other had been the triggerman, but the jury believed Jones, and Atkins was convicted of capital murder and sentenced to die.
Neither the quality of the evidence nor the severity of the crime was in dispute. The question before the court was not what Atkins had done, but what he was. Atkins’s counsel argued before the Virginia Supreme Court that Atkins was mildly mentally retarded, with a measured IQ of 59, and as such could not be held sufficiently morally responsible to warrant the death penalty. The state supreme court rejected this argument, citing the U.S. Supreme Court’s 1989 ruling in Penry v. Lynaugh that capital punishment of mentally retarded prisoners doesn’t violate the Constitution.
This conclusion wasn’t reached without great controversy among the Virginia justices. The constitutional questions involved were difficult enough that the U.S. Supreme Court agreed to revisit the case, and with it Penry. This time, the high court came down on the opposite side. In a 6−3 decision, they ruled that it would be unconstitutional to execute Atkins or any other mentally retarded criminal.
At first glance, this seems weird. The Constitution didn’t change in any relevant way between 1989 and 2012; how could the document first license a punishment and then, twenty-three years later, forbid it? The key lies in the wording of the Eighth Amendment, which prohibits the state from imposing “cruel and unusual punishment.” The question of what, precisely, constitutes cruelty and unusualness has been the subject of energetic legal dispute. The meaning of the words is hard to pin down; does “cruel” mean what the Founders would have considered cruel, or what we do? Does “unusual” mean unusual then, or unusual now? The makers of the Constitution were not unaware of this essential ambiguity. When the House of Representatives debated adoption of the Bill of Rights in August 1789, Samuel Livermore of New Hampshire argued that the vagueness of the language would allow softhearted future generations to outlaw necessary punishments:
The clause seems to express a great deal of humanity, on which account I have no objection to it; but as it seems to have no meaning in it, I do not think it necessary. What is meant by the term excessive bail? Who are to be the judges? What is understood by excessive fines? It lies with the court to determine. No cruel and unusual punishment is to be inflicted; it is sometimes necessary to hang a man, villains often deserve whipping, and perhaps having their ears cut off; but are we in future to be prevented from inflicting these punishments because they are cruel?
Livermore’s nightmare came true; we do not now cut people’s ears off, even if they were totally asking for it, and what’s more, we hold that the Constitution forbids us from doing so. Eighth Amendment jurisprudence is now governed by the principle of “evolving standards of decency,” first articulated by the Court in Trop v. Dulles (1958), which holds that contemporary American norms, not the prevailing standards of August 1789, provide the standard of what is cruel and what unusual.
That’s where public opinion comes in. In Penry, Justice Sandra Day O’Connor’s opinion held that opinion polls showing overwhelming public opposition to execution of mentally deficient criminals were not to be considered in the computation of “standards of decency.” To be considered by the court, public opinion would need to be codified by state lawmakers into legislation, which represented “the clearest and most reliable objective evidence of contemporary values.” In 1989, only two states, Georgia and Maryland, had made special provisions to prohibit execution of the mentally retarded. By 2002, the situation had changed, with such executions outlawed in many states; even the state legislature of Texas had passed such a law, though it was blocked from enactment by the governor’s veto. The majority of the court felt the wave of legislation to be sufficient proof that standards of decency had evolved away from allowing Daryl Atkins to be put to death.
Justice Antonin Scalia was not on board. In the first place, he only grudgingly concedes that the Eighth Amendment can forbid punishments (like cutting off a criminal’s ears, known in the penological context as “cropping”) that were constitutionally permitted in the Framers’ time.*
But even granting this point, Scalia writes, state legislatures have not demonstrated a national consensus against execution of the mentally retarded, as the precedent of Penry requires:
The Court pays lip service to these precedents as it miraculously extracts a “national consensus” forbidding execution of the mentally retarded . . . from the fact that 18 States—less than half (47%) of the 38 States that permit capital punishment (for whom the issue exists)—have very recently enacted legislation barring execution of the mentally retarded. . . . That bare number of States alone—18—should be enough to convince any reasonable person that no “national consensus” exists. How is it possible that agreement among 47% of the death penalty jurisdictions amounts to “consensus”?
The majority’s ruling does the math differently. By their reckoning, there are thirty states that prohibit execution of the mentally retarded: the eighteen mentioned by Scalia and the twelve that prohibit capital punishment entirely. That makes thirty out of fifty, a substantial majority.
Which fraction is correct? Akhil and Vikram Amar, brothers and constitutional law professors, explain why the majority has the better of it on mathematical grounds. Imagine, they ask, a scenario in which forty-seven state legislatures have outlawed capital punishment, but two of the three nonconforming states allow execution of mentally retarded convicts. In this case, it’s hard to deny that the national standard of decency excludes the death penalty in general, and the death penalty for the mentally retarded even more so. To conclude otherwise concedes an awful lot of moral authority to the three states out of step with the national mood. The right fraction to consider here is 48 out of 50, not 1 out of 3.
In real life, though, there is plainly no national consensus against the death penalty itself. This confers a certain appeal to Scalia’s argument. It’s the twelve states that forbid the death penalty* that are out of step with general national opinion in favor of capital punishment; if they don’t think executions should be allowed at all, how can they be said to have an opinion about which executions are permissible?
Scalia’s mistake is the same one that constantly trips up attempts to make sense of public opinion; the inconsistency of aggregate judgments. Break it down like this. How many states believed in 2002 that capital punishment was morally unacceptable? On the evidence of legislation, only twelve. In other words, the majority of states, thirty-eight out of fifty, hold capital punishment to be morally acceptable.
Now, how many states think that executing a mentally retarded criminal is worse, legally speaking, than executing anyone else? Certainly the twenty states that are okay with both practices can’t be counted among this number. Neither can the twelve states where capital punishment is
categorically forbidden. There are only eighteen states that draw the relevant legal distinction; more than when Penry was decided, but still a small minority.
The majority of states, thirty-two out of fifty, hold capital punishment for mentally retarded criminals in the same legal standing as capital punishment generally.*
Putting those statements together seems like a matter of simple logic: if the majority thinks capital punishment in general is fine, and if the majority thinks capital punishment for mentally retarded criminals is no worse than capital punishment in general, then the majority must approve of capital punishment for mentally retarded criminals.
But this is wrong. As we’ve seen, “the majority” isn’t a unified entity that follows logical rules. Remember, the majority of voters didn’t want George H. W. Bush to be re-elected in 1992, and the majority of voters didn’t want Bill Clinton to take over Bush’s job; but, much as H. Ross Perot might have wished it, it doesn’t follow that the majority wanted neither Bush nor Clinton in the Oval Office.
The Amar brothers’ argument is more persuasive. If you want to know how many states think executing the mentally retarded is morally impermissible, you simply ask how many states outlaw the practice—and that number is thirty, not eighteen.
Which isn’t to say Scalia’s overall conclusion is wrong and the majority opinion correct; that’s a legal question, not a mathematical one. And fairness compels me to point out that Scalia lands some mathematical blows as well. Justice Stevens’s majority opinion, for instance, remarks that execution of mentally retarded prisoners is rare even in states that don’t specifically prohibit the practice, suggesting a public resistance to such executions beyond that which state legislatures have made official. In only five states, Stevens writes, was such an execution carried out in the thirteen years between Penry and Atkins.