Anonymous Giving as a Vice: An Application of Image Motivation

doi:10.4236/tel.2012.24071

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Theoretical Economics Letters, 2012, 2, 385-390

http://dx.doi.org/10.4236/tel.2012.24071 Published Online October 2012 (http://www.SciRP.org/journal/tel)

Anonymous Giving as a Vice: An Application of

Image Motivation

Masaoki Tamura

Graduate School of Economics, University of Tokyo, Tokyo, Japan

Email: [email protected]

Received June 6, 2012; revised July 2, 2012; accepted August 1, 2012

ABSTRACT

While some donors boast about their giving, others give anonymously. A novel feature of this paper is that anonymity is

endogenously con trolled by dono rs themselves, not exogenously controlled by fundraisers. Is anonymous giving really

a virtue, as is generally recognised? Paradoxically, this p aper proves that anonymity is a vice for fun draisers even if it is

what donors desire. If many altruists (a good type) switch from known to anonymous giving, it relatively lowers the

group reputation of known donors and enhances that of non-donors. These effects dilute the incentive for other indi-

viduals to become known donors, if they have psychological “image motivation”. I suggest a practical method to con-

trol the expected number of anonymous donors: fundraisers remove the “check boxes” from their web sites.

Keywords: Giving; Anonymity; Altruism; Image; Fundraising

1. Introduction

Many studies, including [1-3], show that if experimenters

control the anonymity of examinees, the examinees

change their prosocial behaviour. The more anonymity

experimenters provide, the less altruistic the examinees

become. A novel feature of this paper is that anonymity

is endogenously determined by the donors themselves.

While some donors boast about their giving, others give

anonymously. Is anonymous giving worth the same as

known giving to fundraisers? Is anonymous giving really

a virtue, as is generally recognised? Paradoxically, this

paper proves that anonymous giving is a vice, even if the

donors themselves desire anonymity.

We extend Benabou and Tirole’s image signalling frame-

work to the case in which “anonymity” is redefined and

individuals themselves choose anonymity level. Since

people care about their social reputations, even non-al-

truists donate to conceal their selfishness and enhance

their reputations. The key lies in this “hypocritical” be-

haviour of donors. Such behaviour is possible because

altruism is private information and the donation amount

is what others observe; giving enables non-altruists to

mimic altruists and achieve recogn ition as altru ists. How-

ever, if we allow donors an option to anonymous giving,

it is clear that not all donors choose the same anonymity

level. It is essential to identify wh o donates anonymous ly,

because it determines whether anonymous giving is in-

dependent of or related to the hypocritical behaviour. Our

result is that those who prefer anonymous giving are the

best “target” for the non-altruists to mimic, and the exis-

tence of anonymous donors negatively affects the hypo-

critical behaviour of non-altruists and the total amount of

donation.

Practically, fundraisers should control the expected

number of anonymous donors. However, we can find one

example that exaggerates the existence of anonymous

donors. Currently, many fundraisers solicit contributions

via the Internet in addition to normal fundraising activi-

ties. On their Web sites, some fundraisers place check

boxes for donors to select anonymous or known dona-

tions. Figure 1 shows how a typical such site looks. On

the page, donors fill out not only the information about

the amount of donation, name, address, and credit card

number but also the check box “I prefer to make this do-

nation anonymously”. By providing the check boxes,

these fundraisers intend to make it convenient to donate

anonymously. The problem, however, is that, when fac-

ing the choice, donors expect that fundraisers provided

the check box in response to many requests from a sub-

stantial number of anonymous donors. In other words,

the check box exaggerates the number of anonymous do-

nors. The contribution of this paper is threefold. First and

foremost, it suggests how fundraising campaigns can be

more efficiently designed: fundraisers should all ow anony -

mous donation only as an exception and should not exag-

gerate the number of anonymous donors. Specifically, we

can identify inefficiency in some fundraising Web sites

and suggest an improvement. Such sites can impose a

small “foot cost” on anonymous giving. Second, this is

the first paper that studies a model in which an onymity is

M. TAMURA

386

Figure 1. Online donation page.

endogenously determined. Here, anonymity is controlled

not by the fundraisers but by the donors themselves. Thus,

we can study the case in which donors choose perfect

anonymity, namely by donating anonymously; almost no

economic studies have addressed this case in detail. Third,

the study gives weight to the heterogeneity of image

motivation among individuals, in contrast to [4]. Thus, we

can identify who donates anonymously

2. Structure of the Model

Let us begin our analysis by specifying the utility function

of the individuals who have both an image motivation

and a warm-glow preference1.







ˆˆ

,,= 1lnlnln

ii iiiiiii

Ucxc x I









(1)

c denotes individual i’s consumption for private goods,

denotes individual i’s donation, i



denotes the

altruism parameter, and i



denotes the self-conscious-

ness of consumer i. Individuals are heterogeneous in the

parameters i



and i



. Because we assume that

individual i’s parameters i



and i



are private in-

formation and unobservable to all other individuals,

others form beliefs about i’s parameters. ˆi



denotes the

belief of other individuals about i’s altruism, i



Individuals derive utility directly from this belief of

others, namely, the extent to which others consider an

individual altruistic. This corresponds to the concept of

self-image or image motivation. The function







re-

presents this image motivation of the individuals. We

assume that and that . People who

are considered socially altruistic have a high i



>0



0=1Iˆ



and

hence high utility. The more altruistic they are con-

sidered the more utility they gain. Here, the hetero-

geneit y lies in altruis m i



and self-consciousness ,

which we specify below. i

beta

The budget constraint for is

ii i

cx y (2)





iiki ia

DxD x (3)

i is the endowment of individual i. People allocate

their income between consumption and donation.

known donation, a

is anonymous donation, and i

is a dummy variable th at takes the value if individual

chooses known over anonymous donation, and takes

the value if individual chooses anonymous over

known donation. In short, in this model, when in-

dividuals want to donate, they must choose between a

known and an anonymous donation. For simplicity, we

assume that individuals cannot make both anonymous

and known donations at the same time. We must draw

attention to the implied assumption that the choice be-

tween anonymous and known donation does not directly

affect the utility: both choices yield the same warm-glow

utility. However, the choice does matter when individuals

form beliefs about others’

i0i



values: ˆi



. ˆi



is formed

ˆki









 (4)

The beliefs about others’ altruism are formed based on

income and known donation. In other words, individual’s

decision variables except known donation are unob-

servable to the others. It must be noted that individuals

form beliefs about i



based on ik

, not i

. This result

is owing to the definitio n of anon ymou s donatio n : anon y-

mous donation is unobservable to others, while known

donation is observable. It is important that anonymous

donors (0



and k) and non-donors (

and ) are considered the same by others.

=0x=0

Next, we specify the parameter values and the dis-

tribution of the individual types in th is economy. Table 1

summarises the information about the four individual

types of our model.

3. The Equilibrium

3.1. Who Gives Anonymously?

The first task is to determine who donates anonymously.

The answer is the “pure altruists”. There are two reasons

for this. First, because anonymous donation, by defini-

tion, cannot be observed by others, anonymous donors

and non-donors are considered the same (i.e. the same

ˆi



). Second, the types who ar e concern ed with their own

reputation (0





) want to be seen as altruistic (i.e., as

donors); consequently, they never prefer anonymous to

known donation. Then, the “pure altruists” (who are

altruistic but not self-conscious) is the only type who

may make anonymous donations. Pure altruists must be

1Theoretical and empirical backgrounds for these two motivations are

given in [4-10].

M. TAMURA 387

Table 1. Individual Types.

Type





Population

Selfish 0 0

Pure Altruist



Hypocrite 0



Impure Altruist





indifferent to whether a donation is known or anony-

mous.

3.2. Equilibrium Actions

From now on, we examine the behaviour of each type to

find the Nash equilibrium of our model. It should be

noted that individuals interact only through the image

(ˆi



) of the types to which they belong. Thus, people

without self-consciousness (i.e., =0



) behave without

considering others’ actions. We first limit our attention to

these types: the selfish and the pure altruists.

3.2.1. Selfis h : &

=0α0β=

People without self-consciousness, by definition, simply

solve their classical optimisation problems with respect

to donation and private good, but not their images. In

short, it is the simple warm-glow setup we see above. It

is obvious that the selfish spend all of their income on

private goods. For the selfish, i

and . =

cy =0

3.2.2. Pure Altrui st: α=α & 0β=

Pure altruists also face their classical optimisation prob-

lems without image motivation. The solution to this

problem is





 and =



. Because ˆi



does not appear in their optimisation problems, pure

altruists are indifferent to the choice between a and

k; both options yield the same utility. Here, we assume

that a fraction of the pure altruists choose

anonymous over known donation, and thus, 1



0,1A





them choose known over anonymous donation. As a

result, the introduction of the option of anonymous

giving makes some pure altruists switch from known to

anonymous giving. We should not overlook that the total

donation amount of pure altruists is independent of

3.2.3. Hypocrite: &

=0αβ=



It is most important to examine the conditions under

which even hypocrites make donations in spite of their

selfish nature. By making donations, th ey mimic the pure

altruists (a good type) to enhance their reputations. Note

that the pure altruists are the best “target” for the hypo-

crites to mimic, becau se the impure altruists are averse to

mimicry as is described later.

It can be checked easily that there are only two options

for hypocrites to choose, or



. If they

choose , then they are in the same group as the

selfish. Conversely, if they choose

=0x=i



, then they

are in the same group as the pure altruists. Comparing the

two options, the condition for hypocrites to choose



over is2 =0x



lnln1

>lnln.

ii hp

ihpas

yy I

NAN

NAN N









 

















(5)

The left hand side represents the utility when hypo-

crites join the group of known donors (=



), while

the right hand side represents the utility when they join

the group of non-donors (). In conclusion, the

more anonymous donors there are, the less likely hypo-

crites are to donate. Let us mathematically confirm this

result and explain the intuition behind it. The second

term on the left hand side of (5) is decreasing in







ln 1<0,

hpa

INAN



















(6)

and the right hand side of (5) is increasing in

>0.

hpas

INANN













 (7)

The interpretation of these two inequalities is the core

of this paper. We refer to (6) as the “decrease effect”, and

(7) as the “blend effect”. We first note that pure altruists

are thought to be a “good” type compared with the

selfish and the hypocrites because pure altruists have

higher altruism. Next, the group reputation is formed

according to the ratio of “good” (altruistic) group mem-

bers. To interpret (6), suppose that some of the pure

altruists (a “good” ty pe) switch from known

(









,=0,

ak i



y) to anonymous donation

(









,= ,0

ak i

xx y



). Such a switch implies a decrease of

a “good’ type in the group of known donors (=



Then, to the hypocrites, joining the group of known

donors (=



) becomes less attractive. This decrease

effect corresponds to inequality (6). The second in-

equality (7) represents the blend effect. Because anony-

mous donation is unobservable, people now think that

some perceived non-donors are actually anonymous do-

nors. Some fraction of non-donors is of the “good” type (

2For simplicity, we consider the case in which all hypo crites behave as

a group. This does not change the result much as long as we focus on

the symmetric equilibrium.

M. TAMURA

388

ˆ=>

hpas

NAN N



 0

do not donate.

3.2.4. Impure Altruist: =



& β=



on the left hand side of (7)). As a result, the existence of

anonymous donors enhances the reputation of non-do-

nors, and joining the group of non-donors () be-

comes more attractive to the hypocrites. Here, anony-

mous donors blend into non-donors. This blend effect

corresponds to inequality (7).

If hypocrites mimic pure altruists, the reputations of the

hypocrites improve, as is described above. In contrast,

the reputations of the pure altruists worsen because they

are now in the same group as hypocrites (a “bad type”).

Even then, the equilibrium action of pure altruists is un-

changed because they do not derive utility from the re-

putation (i.e., =0



A numerical simulation is shown in Figure 2, “Utility

of Hypocrites”3. The “Join Donors” curve corresponds to

the left hand side of (5) for each

. The “Join Non-Donors”

curve corresponds to the right hand side of (5) for each

. We refer to the value of

for which the left hand

side equals the right hand side as *

. If there are

anonymous donors above , then hypocrites

*=17.7%A

Contrary to pure altruists, impure altruists care about

their own reputation (i.e., =



0). Impure altruists

are averse to be mimicry by hypocrites. First, when

below *

, hypocrites mimic pure altruists. If

increasing from 0, then pure altruists become increasingly

less attractive to mimic than impure altruists. In response,

Figure 2. Numerical simulation.

3The values used in o u r numerical simulations are =0.1



, =0.5



=10



, and





ˆˆ

=3 20



.

M. TAMURA 389

impure altruists want to become less attractive because

they are averse to mimicry by hypocrites. Then, impure

altruists gradually increase their donations as

be-

comes large because larger-amount donors are less at-

tractive for hypocrites to mimic. Secondly, when

surpasses *

, hypocrites are non-donors. If

is in-

creasing from *

, for hypocrites, being non-donors

yields increasing utility compared with mimicking im-

pure altruists. In response, impure altruists can decrease

their donation amounts to their original ideal level,



3.3. Total Amount of Donation

While impure altruists are averse to be mimicry by hypo-

crites, pure altruists do not care about it. Thus, the hypo-

crites mimic the pure altruists. The existence of anony-

mous donors means 1) the decrease of the best “target”

for the hypocrites to mimic and 2) the increase of the

“good” type in the non-donor group. The total amount of

donation of these four types is shown in Figure 2. In this

numerical example, . The sharp decrease at

is due to the hypocrites’ behaviour: they no

longer mimic pure altruists. In conclusion, for fundraisers

to raise as much money as possible, it is crucial that

*=0.177A

does not exceed *

, though a small fraction of anony-

mous donors is not harmful.

4. Policy Implication and Discussions

In the preceding section, we examine how the total dona-

tion amount varies according to an exogenously deter-

mined

. This result raises the question, can fundraisers

control

and expected

? Inthis section, we discuss

one practical method to control both

and expected

Currently, many fundraisers solicit contributions via

the Internet in addition to normal fundraising activities.

On their Web sites, some fundraisers including Anna

Marie’s Alliance, the Minnesota Aids Project, and Net-

work for Good place check boxes for donors to select

either anonymous or known donations. Figure 1 shows

how a typical such site looks. Donors fill out not only

information about the donation amount, name, address,

and credit card number but also a check box, “I prefer to

make this donation anonymously”. However, some or-

ganisations, such as the American Cancer Society, the

American Red Cross, and Doctors Without Borders do

not provide such a ch eck box on th eir Web sites. Witho ut

a special request, only known donation is available for

donors. We see that not a few fundraisers explicitly offer

opportunities for anonymous giving. By providing the

check boxes, these fundraisers intend to make it conven-

ient to donate anonymously. The problem, however, is

that, when facing the choice, donors expect that fund-

raisers provided the check box in response to many re-

quests from a substantial number of anonymous donors.

In other words, the check box exaggerates the number of

anonymous donors. Here,

is expected higher than

that it actually is.

To keep both

and expected

below *

, fund-

raisers can remove this type of check box. Instead, they

can implement some type of small foot cost on anony-

mous giving and accept anonymous donations only as an

exception. For instance, to give anonymously, donors

have to send an e-mail to fund raisers in addition to filling

out the personal information form. Then, those who re-

quire anonymity choose anonymous giving with a small

effort, while those who are indifferent to whether the

donation is anonymous choose known giving.

An important experimental finding is reported in [1].

They show that, if examinees give subjects an option to

donate anonymously, subjects increase their giving. Note

that the subjects mainly increase known giving, not ano-

nymous giving. Their finding is not inconsistent with our

theoretical results, because their finding corresponds to

the case of *



in our model. Our model predicts

that if

is small, impure altruists increase known giv-

ing above their ideal amount. This is what [1] observes.

We also predict that if we would make

and expected

sufficiently large, then the subjects would decrease

their known giving. Fundraisers should keep the actual

and expected

at a low level and consequently

maximise the total donation amount.

5. Acknowledgements

I would like to thank Masayuki Otaki for his helpful com-

ments. I am also grateful to Sakuya Tamura for her sup-

port and fruitful discussions.

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