Bounded Rationality, Individual Choice
Social Security Reform as an Example
The Hebrew University of Jerusalem
Presentation at the fall meeting of the American Philosophical
Society, November 14, 2003
The Benefits of Choice
• Economists view choice as something that one can‟t have
too much of, like clean air and beauty.
• Choice supports differentiated tastes and needs and
generates competition among providers, leading to lower
prices (higher quality).
For the benefits of competition to be realized consumers
must be reasonably well informed about price and quality.
The message of the new „Behavioral Economics‟ is:
in many domains people lack stable, well-ordered
preferences. What they choose is a product of framing
effects, starting points and default rules, leaving the
very meaning of preferences unclear(Thaler and
The Rationality of Choices
“People make choices that are in their best interest, certainly
better than choices made by third parties”.
Counter arguments backed by experimental and empirical
research(Thaler and Sunstein,2003): people do not exhibit
rational expectations; fail to make forecasts consistent with
Bayes‟ rule; use heuristics that lead them to make systematic
blunders; exhibit preference reversal; suffer from problems of
[Rates of obesity in the U.S. exceed 20 percent and over 60
percent are either obese or overweight. Obesity leads to
serious health risks, frequently leading to premature death.
Experts agree that these reflect problems of self-control and
short sightedness as well as ignorance].
• Framing effects. Concerning a risky medical procedure,
when people are told “of those who have this procedure,
90 percent are alive after five years” they are far more
likely to agree to the procedure than when they are told
that “of those who have this procedure, 10 percent are
dead after five years” [Tversky-Kahneman].
• Starting-Point Effect. Most 401(K) plans use an opt-in
design, employees filling an enrollment form to join. The
alternative is automatic enrollment, employees receiving
the same information, but are told that they may register to
Moving from the former to the latter method, enrollments
were found to jump from 49% to 86% [Madrian and Shea,
Should the adoption of automatic enrollment be considered
Preferences seem to depend on domain and context.
Choosing a default may be avoided if employees are
required to make a choice („coerced choosing‟). Should
people have the freedom to procrastinate?
Another study illustrates the attraction and importance of
default options [Johnson et-al, 1993] . Buyers of auto
insurance in New Jersey and Pennsylvania were given a
choice whether to pay lower rates in exchange for reduced
rights to sue for pain and suffering. In Pennsylvania, the
default was the full right to sue, with a rebate for accepting
reduced rights. In New Jersey, the default was a limited right
to sue with a surcharge to get the full rights. In both states,
about 75-80 percent of drivers took the default option.
Presumably, most people were “deciding not to decide”.
Another important example: the appropriate default rule for
organ donations (Johnson and Goldstein,2004). In many
nations – Austria, Belgium, Denmark, Finland, France, Italy,
Luxemburg, Norway, Singapore, Slovenia and Spain –
people are presumed to consent to allow their organs to be
used after death for the benefit of others, but they are
permitted to rebut (on their drivers licenses) this
presumption. In the U.S. (and Israel), in contrast, those
who want their organs to be available for others must
affirmatively validate their choice (also on their drivers
In the „presumed consent‟ countries over 90 percent of the
people make their organs available for donation, while in
the U.S. it is below 20 percent. We predict that the
European default rule if applied in the U.S. would produce
European-Style donation rates.
The default rule for organ donation does not fit the usual
definition of paternalism since it concerns the welfare of third
parties, not of choosers. With respect to behavior, however,
the analysis is similar.
Which default rule better promoters welfare?
In this case, coerced choice may reveal the „true‟ preference.
• Is Paternalism inevitable? In many situations, some
organization or agent must make a choice that will affect the
preferences and behavior of others. Peoples‟ preferences
often do not predate the choices made by planners
Some libertarians will accept efforts by private firms, but not
by the government, to steer people‟s choices because
market pressures are thought to impose protection against
Trade off Contrast: Choice dependence on ‘context’
Contrast effects are ambiguous in perception and judgment.
A circle appears large when surrounded by small circles and
vice-versa. Simonson and Tversky (1992) have shown that
the contrast effect applies not only to single attributes but
also to the trade-off between attributes. In an experiment,
they examined the trade-off between quality and price.
When subjects were given background information –
(background A) about expensive (pricewise) exchange rates
between computer memory and prices they tend to choose
larger computer memories compared to subjects who are
given background information about cheap exchange rates
between these attributes.
The Importance of Bounded Rationality and Choice
in Social Security (SS) Reform
Can individuals be considered as „rational‟ when it comes to
long-term savings for retirement?
The „Reasonable Person‟ approach:
Consider an individual who works and saves for 30 years
(age 35-64) and then retires for 15 years. When working,
he/she has a constant income flow, Y.
With a constant savings rate s and interest compounded
continuously at rate i, wealth at age t, Wt , is:
sY (t -35)i
Wt = (e - 1)
The constant annuity that can be financed for 15 years out of
W65 is 15i
A = iW65
(e15i - 1)
Setting the replacement rate,
A , at ⅔ , implies the
(1 - s ) y
Interest rate 0 .01 .02 .03 .04
Savings rate .25 .21 .17 .14 .12
Wealth/income at 65 6.5 6.0 5.6 5.3 4.9
With an income growth rate of 2%, constant retirement
benefits after retirement and a 2/3 replacement rate for
consumption at age 60, the numbers are not much different:
Interest rate .02 .03 .04
Savings rate .21 .17 .17
Wealth/income at 65 5.2 4.9 4.6
Now, let‟s look at the actual data derived from the Social
Security Data base:
Percent of married Men 58 – 63, in 1969, with No Pension
Earnings Level ≤1 ≤2
Under 2500 74.7 76.4
2500 - 5000 26.4 29.6
5000 – 7500 14.6 30.0
7500 – 10,000 13.1 26.8
10,000 – 12,500 7.7 17.6
12,500 – 15,000 - 11.8
15,000 – 25,000 2.7 13.7
25,000 and up 2.6 13.1
Summary: 10 – 15 percent of the population have
a wealth-earnings ratio below one and 30 percent
have a ratio below 2.
Other data exhibits even higher percentages
• Under the current SS system, individuals have almost no
choice except when to start claiming benefits once eligible.
* 5/9 of one percent higher
benefits for each month
delay in retirement
(about 6 percent annually).
• Reform proposals are to shift part of (mandatory) SS
contributions to personal accounts which will be invested
in the market. The cumulative returns will determine the
level of retirement benefits („Defined Contribution‟ system,
in contrast to the current „Defined Benefit‟ system).
What trade-offs will people be offered and how might they
• One or more accounts (programs) allowed?
• Division between stock and bonds (in TIAA-CREF,
specific investments are made by the fund)?
• Choice between single or joint accounts (dividing family
income between spouses)?
• Possibility to combine retirement with other insurance,
e.g. Life Insurance (general issue of survivors‟ benefits)?
• Should withdrawals before retirement for specific purposes
(such as unemployment insurance, recently suggested by
Stiglitz) be allowed?
• Purchase of deferred annuities be available (when, how
much, type of annuities)?
• Choice of fee structure (front loading, management fees or
combination of formulas)?
• Add-On options
• Early eligibility – partial retirement and delayed retirement
• How many types of annuities (x-year certain, single-joint
• Indexation choice (nominal, CPI, Wages)
• Mandatory full or partial annuitization (programmed
withdrawals), maintaining a minimum replacement rate?
• Who will be licensed issuers of annuities and providers of
benefits (SS, pension or insurance firms)?
• Will there be choice between different benefit profiles over
How Much Choice: Modelling Bounded Rationality
“It is easy to talk about bounded-rationality but it is difficult
to model it in a disciplined way” (Mirrlees).
• The Multinomial Logit Model
Probabilistic choice among a finite number of discrete
Choice probabilities are based on Luce‟s “Choice Axiom”
(a „path-independence‟ axiom).
Probabilities depend on the domain (choice alternatives).
Luce‟s Theorem states, roughly, the following.
Suppose individuals are identified by a preference
parameter θ ≥ 0 (attitude to work, health,…). Facing n
alternatives, the probability that individual θ chooses
alternative i, Pi(θ), is given by
qui (q )
Pi (q ) = n
e qu j (q )
where ui, i = 1, 2,…, n, are scalar functions („utility‟).
The parameter, q > 0, exhibits the precision of
choice: when q = 0 all alternatives have equal
1 , when q → each individual chooses
the most preferred alternative:
argmax [u1, u2,…un].
There is an aggregate distribution of individual types (θ).
The government knows this distribution but cannot dictate
Individuals‟ welfare is measured by expected-utility.
An increase (decrease) in the domain (number of
alternatives) exacerbates (reduces) the errors made by
individuals but improves (worsens) the welfare of those who
prefer the added (eliminated) alternatives.
Suppose that social welfare is utilitarian, i.e. it positively
depends on the sum of individuals‟ welfare.
(a) When q is „large‟ (for all individuals) then the full set
of alternatives is always optimal.
(b) When q is „small‟, it is always optimal to entirely
eliminate individual choice [the „shrinking‟ of the
choice-set is monotone in q].
Calculations indicate that it is desirable to eliminate
individual choice at surprisingly low levels of errors.
[Two alternatives (1, 2). Two homogeneous groups of
individuals: group 1 (2) prefers alternative 1 (2).
The critical statistical type I and type II errors that lead to
elimination of one of the two alternatives are extremely
Objections to ‘Libertarian Paternalism’
Although the arguments for libertarian paternalism seem
compelling ( this term, and the following discussion, was put
forward by Thaler and Sunstein(2003)), we wish, in closing,
to respond to certain concerns:
• This is a start of a „Slippery-slope‟. Once one grants that
default rules („cafeteria lines‟) should be designed
paternalistically, there will be an onslaught of intrusive
Three responses: (1) in many cases there is no alternative
to paternalism (in the weak sense); (2) opt-out rights can
limit the steepness of the slope; (3) if planners, bureaucrats
and managers suffer from self-control problems, so do
• Planners are often unable to make sensible choices,
because they lack the incentives created by market
• An argument in the opposite direction: based on
evidence of bounded rationality and self-control problems
in many domains, people should not be given the
freedom of choice because they choose poorly.
These complex philosophical issues of value and fact we
have to leave open in this talk.