11.7.10

Sandwich.

11.2.10

Thought you guys might enjoy this :)

One (wannabe) economist’s approach to home teaching (hehe):

Home teaching: a conundrum familiar to all members of the LDS church and the cause of more than a few grey hairs to Bishops worldwide. And how to solve it? Perhaps game theory can provide some insights.

I have sat through a fair amount of priesthood lessons where beloved leaders have gone on for several minutes appealing to my conscience in an attempt to push me towards doing my home teaching. Sometimes it can even have the opposite effect. And so this Sunday as I was sitting in Elder’s Quorum it came as no surprise to once again hear the Bishop start talking about home teaching. However, this time, as my thoughts began to wander, I found myself thinking, “I wonder if guilt really is the most effective encouragement strategy.” And so, like an self-respecting nerd, I build the following model using game theory.

I figure that leaders use two main strategies: reporting (enforcing) and not asking (not enforcing) which I will denote as (R) and (D). Home teachers also have two strategies: teaching (T) and not teaching (N). The two-player game can be represented as follows:

		LEADERSHIP
		Reporting (R)	No reporting (D)
HOME TEACHERS	Teach (T)	a1, a2	b1, b2
	Don’t teach (N)	c1, c2	d1, d2

Now, given a rational choice assumption, I would expect the following relationships to hold:

a₁ > c₁

(teachers would rather have taught if asked to report)

d₁ ≥ b₁

(some teachers may be indifferent, but most would rather not do their home teaching if they don’t have to report)

b₂ > a₂

(leaders would rather not have to go through so much reporting if the teaching is getting done)

c₂ > d₂

(leaders prefer to be notified if teaching is not being done)

And so, assuming mixed strategies, let p = the probability of teaching and q = the probability of employing a reporting structure. So, solving for p:

a₂p + c₂ – c₂p = b₂p + d₂ – d₂p

p(a₂ – c₂ – b₂ + d₂) = d₂ – c₂

p = (d₂ – c₂)/(a₂ – c₂ – b₂ + d₂)

And for q:

a₁q + b₁ – b₁q = c₁q + d₁ – d₁q

q(a₁ – b₁ – c₁ + d₁) = d₁ – b₁

q = (d₁ – b₁)/(a₁ – b₁ – c₁ + d₁)

Shocking, I know. It would appear the appealing to guilt and other such emotions (increasing the costs of not teaching—i.e. decreasing c₁ and d₁) actually has no effect on the probability of teaching. In fact, it has some adverse effects according to this model:

1.      Since d₁ ≥ b₁, the teachers on the margin may actually get less of a payoff for teaching when no reporting is taking place.

2.      Since a –c₁ is in the denominator of q, using guilt tactics will actually decrease the probability of employing a reporting structure.

3.      Since neither c₁ nor d₁ factor into the probability of teaching (p), teaching in unaffected.

Now, you may be asking: then how do we increase the probability of teaching? And the answer is, not surprisingly, to increase the payoffs within reporting structures. That is, to give report-gatherers a higher payoff for collecting reports (i.e. increase a₂ and c₂), thereby increasing enforcement which will cause the probability of teaching to increase.

However, if leaders are keen on the increasing the costs of not teaching (decreasing c₁ and d₁), I would suggest public reporting. That is, asking members publicly if they have done their home teaching and, if not, if they have plans to do so. This would certainly decrease enforcement, but perhaps not by a significant amount since the costs there associated would be smaller. Another tactic with similar results might be to, every Sunday, announce the names of those that have not yet taught that month.

As far as increasing the payoffs associated with reporting, I would suggest playing the “reporting” strategy with probability 1 along with moment randomization. That is, announcing that report-gatherers will call once a week and then randomly selecting when they call. This would hopefully induce teachers to form strategy expectations while also washing out some avoidance strategies. Also, although a reward system for report-gatherers might not seem ethical, not all rewards need be material. Bishops might think of simply calling and thanking those report-gatherers who were faithful in calling every week. This would increase the benefits associated with reporting and would thereby increase enforcement—consequently improving the teaching dynamic of the ward.

Now, the current teaching dynamic of my ward, as reported on Sunday, is about 50%. What does this say about reporting structures? Although there are several combinations, I might suggest the following:

R if T	R if N	D if T	D if N
a2 = 3	c2 = 1	b2 = 4	d2 = 0

Substantively, this means that my ward gets a high payoff if teaching is done, but absolutely hates reporting when teaching has not been done—this implies high social sanctions (i.e. awkwardness) in regards to reporting or could imply that the costs of reporting are high in relation to the benefits of teaching. Either way, this (wannabe) economist would suggest increasing c₂ at all costs—report-gatherers must be at least indifferent in their report-gathering preferences (c₂ ≥ a₂) in order to maximize teaching.

Cheers.

:D