H. Spencer Banzhaf, The Cold-War Origins of the Value of Statistical Life (VSL), Part II
To understand the origins of the VSL, we must back up some 25 years before Schelling's essay,
to the very first years of the RAND Corporation. Officially opening in 1946 as "Project RAND,"
it began as a small think tank internal to the Douglas Aircraft Company with funding from the
USAF. Its primary purpose was to forge an interdisciplinary, integrated study of the engineering
of weapons systems and the study of military strategy: the acronym is for "Research ANd
Development." Because of the inherent conflict of interest in an aircraft company appraising
military hardware and strategy, RAND soon became independent in 1948 with support from the
Ford Foundation. [5]
From its early focus on science and engineering, RAND soon showed increasing interest
in economics and policy studies. Warren Weaver, a member of RAND's board, established a
research section on the "evaluation of military worth," patterned after his Applied Mathematics
Panel (AMP), which was viewed as a success in WW II (Leonard 2010, Mirowski 2001). The
idea, explained Weaver, was to explore "to what extent it is possible to have useful quantitative
indices for a gadget, a tactic or a strategy, so that one can compare it with available alternatives
and guide decisions by analysis…" (quoted in Kaplan 1983 72, emphasis added). Weaver quickly
brought in his protégés from the AMP, John Williams and Edwin Paxson. In previous work
for the Naval Ordnance Test Station, Paxson had worked with John von Neumann to model a
submarine-destroyer duel, possibly the first application of formal game theory to military problems.
In that particular application, the payoffs were tons of shipping saved or lost. In general,
though, similar quantitative measures of the costs and benefits were required to subject a choice
to RAND's vision of rigorous OR.
Weaver also brought in a number of economists. Among the first were Allen Wallis and
Armen Alchian, who began to work with RAND as early as 1946. By 1948, the economists were
constituted as their own division inside the section on evaluation of military worth. The division
was headed by Charles Hitch, who in turn brought in Stephen Enke, Jack Hirshleifer, Roland
McKean, David Novick, and Albert Wohlstetter (Jardini 1996, Leonard 2010, Mirowski 2001).[6]
Meanwhile, Paxson began a project on strategic bombing, constructing a special Aerial
Combat Research Room to simulate aerial maneuvers in a game-theoretic context. By 1947, he
and Williams found the computational requirements of their research so demanding that they,
along with von Neumann, persuaded RAND to acquire one of the first EDVAC binary computers
for their work. Soon, too, George Dantzig was on the scene to apply his simplex algorithm
for linear programming (Jardini 1996 86, Mirowski 2001 212). In this way, RAND was reshaping
OR and economics in the image of John von Neumann, while using the latest and most
powerful technology available. These were heady times.
RAND's first big opportunity to showcase its new analytical capabilities came in 1949,
shortly after the Soviet Union detonated its first atomic bomb. The USAF asked RAND to apply
systems analysis to design a first strike on the Soviets. The "Strategic Bombing Systems Analysis,"
led by Edwin Paxson, attempted to use operations research methods to find the optimal mix
of atomic bombs and bombers (Jardini 1996, Hounshell 1997). Specifically, it sought to solve a
classic OR problem formulated in terms of choosing bombs and bombers to maximizing damage,
subject to a fixed dollar budget (to procure, operate, and maintain the force) and fixed budget of
fissile material (Jardini 1996 54).[7]
As discussed by Kaplan (1983) and Jardini (1996), Paxson and RAND were initially
proud of their optimization model and the computing power that they brought to bear on the
problem, which crunched the numbers for over 400,000 configurations of bombs and bombers
using hundreds of equations. The massive computations for each configuration involved simulated
games at each enemy encounter, each of which had first been modeled in RAND's new
aerial combat research room.[8] They also involved numerous variables for fighters, logistics,
procurement, land bases, etc. Completed in 1950, the recommended solution to this optimization
problem was to fill the skies with numerous inexpensive and vulnerable propeller planes, many
of them decoys carrying no nuclear weapons, to overwhelm the Soviet air defenses. Though
losses would be high, the bombing objectives would be met.
While RAND was initially proud of this work, pride and a haughty spirit do go before a
fall. RAND's patrons in the USAF, some of whom were always skeptical of the idea that pencil-necked academics could contribute to military strategy, were apoplectic. RAND had chosen a
strategy that would result in high casualties, in part because they had given zero weight to the
lives of airplane crews in their objective function, as they seemingly could not be quantified
(Hirshleifer 1950, Jardini 1996). In itself, this failure to weigh the lives of crews offended the
USAF brass, many of whom were former pilots. But moreover that failure led RAND's program
to select cheap propeller bombers rather than the newer turbojets the USAF preferred.[9] For all of
RAND's scientific equations, modern computing power, and vain boasting, in the eyes of its
USAF patrons its first product was a classic case of garbage in, garbage out.
RAND adapted to this debacle in three ways. First, in the short run, recognizing that its
first major study could well prove to be its last, RAND quickly retreated and adopted a more
humble posture. To cut its losses, RAND rushed a follow-up study, this one from Paxson's
assistant Edward Quade, which incorporated some of the criticism from the Pentagon. In particular,
it narrowed the question to the choice of bomber type, adopted the USAF's attack plan, and
assumed the possibility of multiple strikes (Jardini 1996 64).
At the same time, RAND quickly altered course for its proposed second major project,
this one on air defense systems analysis. Headed by Edward Barlow, the first draft of this project
proposal had been a massive 100-page document filled with lots of math, but with dangerously
simple assumptions, such as a single strike and a lack of submarines. As RAND began to
feel the full force of the USAF's displeasure, the proposal was cut to a slim 16 pages, devoid of
offending expressions or arrogant self-confidence in its own scientific method (Jardini 1996 67).
Indeed, Barlow explicitly admitted that a weakness with their approach was the potential to
ignore non-quantitative factors. "The great dangers inherent in the systems analysis approach,"
he said, "are that factors which we aren't yet in a position to treat quantitatively tend to be omitted
from serious consideration" (1950, cit. Jardini 2006 67). It is a lesson that was to be emphasized
by many early advocates of linear programming methods. [10]
Second, as a matter of long-run strategy, RAND reacted to the debacle of the strategic
bombing analysis by diversifying its research portfolio outside of military work. Realizing that
all its eggs were in one very risky basket, RAND looked for research sponsors outside the Pentagon. Over time, it increasingly diversified into work in health, education, and other areas of
social policy. Jardini (1996) explores these moves in some detail, dating the decisive steps as
occurring in the mid to late 1960s. In fact however, they occurred earlier. As early as 1952, the
Ford Foundation provided RAND with a $1m grant to begin a new program, known as RANDSponsored
Research, to take up non-military topics "in the public interest" as well as military and
geo-political topics. The earliest non-military work seriously occupying RAND staff appears to
have been applied work on water resources (De Haven and Hirshleifer 1957, Hirshleifer, De
Haven, and Milliman 1960), followed by projects in transportation and education begun around
1960 (Goldstein 1961).[11]. Interestingly—and likely not coincidentally—when Hirshleifer and
other RAND economists took up water resources they were explicitly entering a research area
where the problem of missing prices, or what resource economists call non-market valuation,
was one of the main topics motivating contemporary literature (Banzhaf 2009, 2010).[12]
Most importantly for this story, RAND's third response to the debacle was to delve deeper into this question of non-market valuation, that is, to try to put actual weights on airplane crews in its objective functions. Inside RAND this came to be known as the "criterion problem"— essentially the problem of specifying what today are often called "indicators" for imperfectly observed or measured objectives, on both the cost and the benefit side. This was the perfect opening for RAND's economists to exploit (Leonard 1991). Jack Hirshleifer was particularly fast off the mark, expressing his opinions on the debacle in internal memoranda almost immediately (Hirshleifer 1950).
From Hirshleifer's perspective, the bombing study failed because of two issues, both of which economists understood well. The first was the distinction between short-run and long-run analysis. Paxson's bombing study imposed unnecessary constraints on the problem, especially the available quantity of fissile material. In the short-run, such constraints may be reasonable, but for long-run strategic planning, they should be subsumed in the budget constraint. That is, given the monetary resources, and enough time, one could acquire more fissile material. The needless constraint on fissile material, coupled with a large monetary budget, contributed to the use of numerous decoy planes serving little purpose except to be shot down (Hirshleifer 1950).
Most importantly for this story, RAND's third response to the debacle was to delve deeper into this question of non-market valuation, that is, to try to put actual weights on airplane crews in its objective functions. Inside RAND this came to be known as the "criterion problem"— essentially the problem of specifying what today are often called "indicators" for imperfectly observed or measured objectives, on both the cost and the benefit side. This was the perfect opening for RAND's economists to exploit (Leonard 1991). Jack Hirshleifer was particularly fast off the mark, expressing his opinions on the debacle in internal memoranda almost immediately (Hirshleifer 1950).
From Hirshleifer's perspective, the bombing study failed because of two issues, both of which economists understood well. The first was the distinction between short-run and long-run analysis. Paxson's bombing study imposed unnecessary constraints on the problem, especially the available quantity of fissile material. In the short-run, such constraints may be reasonable, but for long-run strategic planning, they should be subsumed in the budget constraint. That is, given the monetary resources, and enough time, one could acquire more fissile material. The needless constraint on fissile material, coupled with a large monetary budget, contributed to the use of numerous decoy planes serving little purpose except to be shot down (Hirshleifer 1950).
The second problem Hirshleifer emphasized was missing prices. The basic idea of linear
programming, Hirshleifer reasoned, was to maximize net benefits, which in turn is analogous to
maximizing profits. But profits can be maximized in practice because sales and inputs are priced
in dollars, so revenues and costs are in common coin. Unfortunately, in military applications like
the bombing study, prices were missing from both sides of the ledger. On the benefits side there
was the question of quantifying damage to the enemy. But, said Hirshleifer, the main question
raised by the bombing study centered on the "cost concept (dollars, crews, or planes) to be used"
(Hirshleifer 1950).
Hirshleifer noted that airplane crews can be priced by the cost of training and replacing
them, but we may "set a value on human life higher than the mere training cost of a replacement."
A man may cost $10,000 in terms of a training cost to replace, but we may prefer to lose $15,000 in materials or machines if we can save the man. This sentence points the way to costing loss of men, if the condition described actually holds true. Obviously, there is a limit to the materials or machines we will sacrifice to save the man, and our losses in men should be valued in terms of this limit, cold-blooded as it may sound. In many respects lives and dollars are incommensurable, but unfortunately the planners must compare them. (Hirshleifer 1950 5)
Hirshleifer followed up on this issue along with other economists (including Alchian,
Enke, and Hitch) a few months later. "In our society," they wrote,
personnel lives do have intrinsic value over and above the investment they represent. This value is not directly represented by any dollar figure because, while labor services are bought and sold in our society, human beings are not. Even so, there will be some price range beyond which society will not go to save military lives. In principle, therefore, there is some exchange ratio between human lives and dollars appropriate for the historical context envisioned to any particular systems analysis. Needless to say, we would be on very uncertain ground if we attempted to predict what this exchange ratio should be." (Alchian et al. 1951 20)
In the short term, RAND's best response to this dilemma was to let go of its goal of a
general theory of air warfare, and instead focus on smaller subsidiary problems where apples
could be compared to apples. Incommensurables—like dollars and human lives—would not
need to be compared in the "sub-problem" (Alchian et al. 1951). The basic notion was to isolate
a smaller portion of the system to be analyzed, taking one set of variables as given, and maximize
the objective over the remaining variables, taking the first set as constraints in the problem.
The results of such "sub-optimization" would not be fully optimal, as the tradeoff between the
two sets of variables would not be optimized, but it would be efficient. To put it in other terms,
the analyst could simply trace out the efficient frontier between dollars and lives. Ultimate
decision makers in the Pentagon or the civilian government could eventually make the call (Alchian et al. 1951, Hitch and McKean 1960 Ch. 10). [13]
This notion of sub-optimization was a major theme in much of Hitch's work and his colleagues' for the next decade, and the example of the lives of bomber crews remained the quintessential example motivating the work (Hitch 1953, 1955, Hitch and McKean 1960, McKean 1963). For example, discussing "incommensurables," Hitch and McKean (1960) considered "the comparison of alternative strategic bombing systems that are to be maintained in a state-ofreadiness to deter attack" (185). In this context they further supposed
Hitch and McKean suggest this is a problem if high casualty rates affect morale but also because "we are interested in lives for their own sake" (183). Although it was no longer on the front burner, clearly the problem raised by Paxson's strategic bombing study was still simmering at RAND ten years later.
That said, the wisdom of seeking "missing prices" so that incommensurables like dollars and human lives could be put into the same equation was not a settled matter at RAND. For their part, Hitch and McKean thought it ought not to be attempted. Precedents for valuing human life based on the values of past decisions, court awards, foregone income, or the cost of life-saving "may be useful in particular problems, but none provides a generally valid and appropriate measure of 'the' value of human life" (1960 184). They recommended several variations on the vector approach of calculating the efficient frontier, identifying the tradeoffs among incommensurables, rather than optimizing by choosing from the frontier.
Others were more hopeful that the seeming incommensurables could be made commensurate by examining the revealed preferences of the USAF. Ten years earlier than Hitch and McKean (1960), Alchian et al. (1951) had made many of the same points (Hitch was one of the six authors), but argued that, once the efficient frontier is identified,
Note two things in this passage. First, Alchian et al. presumed that it is the responsibility of the USAF to make the tradeoffs between lives and machines. Second, all effort should be made to understand those "exchange ratios" and build them into the design phase, rather than merely to present decision-makers with an efficient frontier to choose from. That effort would soon come from Thomas Schelling and his student Jack Carlson.
This notion of sub-optimization was a major theme in much of Hitch's work and his colleagues' for the next decade, and the example of the lives of bomber crews remained the quintessential example motivating the work (Hitch 1953, 1955, Hitch and McKean 1960, McKean 1963). For example, discussing "incommensurables," Hitch and McKean (1960) considered "the comparison of alternative strategic bombing systems that are to be maintained in a state-ofreadiness to deter attack" (185). In this context they further supposed
that the preferred (that is, minimum-cost) method of achieving the objective is expected to involve the loss of more lives than some alternative method that is more expensive in dollars—even when the costs of recruiting and training the additional personnel required are included…." (183)
Hitch and McKean suggest this is a problem if high casualty rates affect morale but also because "we are interested in lives for their own sake" (183). Although it was no longer on the front burner, clearly the problem raised by Paxson's strategic bombing study was still simmering at RAND ten years later.
That said, the wisdom of seeking "missing prices" so that incommensurables like dollars and human lives could be put into the same equation was not a settled matter at RAND. For their part, Hitch and McKean thought it ought not to be attempted. Precedents for valuing human life based on the values of past decisions, court awards, foregone income, or the cost of life-saving "may be useful in particular problems, but none provides a generally valid and appropriate measure of 'the' value of human life" (1960 184). They recommended several variations on the vector approach of calculating the efficient frontier, identifying the tradeoffs among incommensurables, rather than optimizing by choosing from the frontier.
Others were more hopeful that the seeming incommensurables could be made commensurate by examining the revealed preferences of the USAF. Ten years earlier than Hitch and McKean (1960), Alchian et al. (1951) had made many of the same points (Hitch was one of the six authors), but argued that, once the efficient frontier is identified,
Presumably it will be the responsibility of the Air Force or the [Joint Chiefs of Staff] to select one of the points as the most sensible one. Of course, any such selection implies a definite exchange ratio between lives and dollars. If this ratio could be revealed to the designers of bombing systems at an early stage they could explicitly determine the most effective system in terms of job done for a combined cost. While probably impossible in this particular case, we ought to avoid whenever possible the presentation of results only in efficient combination form. This yields the weakest possible ordering of the results given minimum rationality assumptions. All effort should be made to utilize whatever information we have about the relative values of the various inputs. (29)
Note two things in this passage. First, Alchian et al. presumed that it is the responsibility of the USAF to make the tradeoffs between lives and machines. Second, all effort should be made to understand those "exchange ratios" and build them into the design phase, rather than merely to present decision-makers with an efficient frontier to choose from. That effort would soon come from Thomas Schelling and his student Jack Carlson.
