Tag: rape

Frameworks for evaluating values

I recently came across a very interesting 2001 paper by Daphne Koller that dealt with influence diagrams and how they could be applied to game theory.  I came across the paper while doing some background reading on a talk on decision making in accordance with our core values by a friend of mine, Somik Raha.

Influence diagrams are a formalism (very similar to probabilistic graphical models) that are used for making decisions.

What Somik Raha has attempted to do is come up with a framework for making decisions while also taking one’s values into account (either as constraints or as inputs into the decision model).  To do that he proposes extensions to influence diagrams.

What I found interesting when I thought about Daphne Koller’s work and Somik’s together, is that they could possibly give you a framework to evaluate your values.

Koller’s formalism reduces to a game theoretic model, which can be evaluated to determine the outcome of the decisions made by a group of people.

Plug in a formalism based on Somik’s ideas and you just might be able to create a way to quantity the benefits of values.

The Importance of Values?

I have been thinking a bit about values these days because there has been a horrific gang rape in Delhi, and there have recently been numerous incidents of bad driving where friends of mine have been injured in Bangalore.  Then there is corruption.  Our society seems to be quite happy with inequality and vast differences in the distribution of wealth.  It make me wonder if our values are to blame.

I have often wondered whether some of our problems originate in our value systems and whether the value systems that we consider sacrosanct in India are really very good ones.

Let me take just a couple of values that most Indians would consider to be very good values

  1. Non-violence
  2. Obedience

and let’s discuss them in more detail.

  1.  Non-violence

This value appeals not just to people in India.  You see variants of the value of non-violence appear in Tolstoy’s writings and in Semitic religions, as you can see from the Bible (“turn the other cheek”) and the Quran (“give alms to one who begs from you, even if he comes on the back of a horse”).

The issue with this sort of value is that it makes a person (and those around him/her) extremely vulnerable to injustice.

In India, we restrict the liberty of women – in their choice of clothing, company and lifestyle – for fear that they could be in danger if they violated societal norms.  This shows that none of us want to fight society or cross swords with someone who might make disparaging comments about personal choices.

Moreover, possibly as a result of the value of non-violence, very few Indians if any are taught fighting skills in school.  So, even if a person really wanted to act, say to protect a friend, he or she might not really have the skills to take down an aggressor.

So, instead of protecting and standing up for people who might be vulnerable, we become their tormentors and make their lives more miserable, just so we don’t have to get our hands dirty, or because we don’t have the skills and strength to do squat.

I’ve written about how bribes are openly collected by traffic policemen.  It should be very easy to put a stop to such behavior if you’re willing to fight.

If non-violence is not a core value, then how do we protect people from tearing each other to bits?

We could start with a question like:  non-violence for what purpose?  (turning it into an extrinsic value)

If the answer is something like, “so that the weak feel protected”, why not make protecting the weak our core value?

I’d prefer teaching kids values like “Don’t ever turn your back on a bully” rather than values like “Don’t fight anybody, and just come home safe, child!”

2.  Obedience

Indian parents love to boast that their child is “such an obedient child!”

Is that a good thing?

Obedience is different from politeness or respect.  The latter are mutual but the former is one way.

So, the politics of obedience creates a hierarchy of subservience.

In India, Parents expect complete obedience from Children.

The Police expect complete obedience from People.

The Politicians expect complete obedience from Police.

Teachers expect complete obedience from Students.

Managers expect complete obedience from Employees.

The creation of the hierarchy (through expectations of obedience) can be very dangerous in many ways.

1.  It can stifle creativity and problem-solving ability.  There is a bias against ideas flowing up a hierarchy because those higher up the hierarchy claim their place above those required to be obedient to them on the premise that they are somehow superior to those below them.  A good example is how parliament will not accept that people have a right to demand a bill against corruption (members of the Indian parliament claim that parliament is supreme in a parliamentary democracy – not the citizens that the parliamentarians represent).

2.  It can leave young people ill-equipped to defend their personal spaces.  I read in a paper on rape that many rapists approach victims by testing their boundaries.  They make comments and otherwise violate the intended victim’s personal boundaries.  If these are not strongly resisted, the probability of an assault becomes greater.  Another strategy used by rapists is to move their intended victim to a new location where they are more vulnerable. It is very important for people to be conditioned so that they do not obey an order by an attacker to relocate under any circumstances.

3.  The hierarchies perpetuate the power of stronger (bigger, older or richer) parties by providing social sanction to their dominant position, and so hinder social mobility.

4.  The obedience hierarchy could allow a few people at the top to amass too much power. It might have, for example, prevented cops from disobeying those in power during the Gujarat riots.

5.  Obedience means valuing rules above truth.  Obedience implies not challenging the rules or the status quo.  So there is little scope for discovering if the rules really are good ones for everybody.  People often defend something they assert with a “because I said so.” – that is, you are expected to believe them because of their authority, and not because they can substantiate their assertion.

Obedience as an absolute value is not entirely harmless.  It could be dangerous to us as a society because corrupt politicians can use the pliability and obedience of people around them to get away with evil (remember the activist who was hacked to death on the orders of a corporator from Bangalore, the journalist who was burnt to death in Uttar Pradesh, or the shutdown that the former Chief Minister of Karnataka State ordered when he was about to be investigated for corrupt dealings?).

I’d love to replace “obedience” with something else, perhaps “honesty” and “trustworthiness” and “pride”.

Summary

I understand that we as Indians are very proud of our values but I’ve tried to argue that our values need to be re-examined.

Personally, I’d love to see the day when we replace all our values with just the value of trustworthiness.

Trustworthiness as a value would mean we’d fight for each other.  It would mean we’d protect the weak.  It would mean we’d be on time.  It would mean we’d be honest.  It would mean we’d be capable and skilled and strong.  It would mean we’d be proud of each other.  It might mean we’d never lose another war.

Reading Koller’s and Somik’s work you get the feeling that one day you might be able to evaluate the comparative benefits of two sets of values, and pick the better one, using plain math.

And hopefully, by showing them mathematical proofs, you can convince people to change their values and pick better ones for themselves.

Quantum of Punishment – Or Should Draconian Punishment Ever be Used?

One of my friends – Nishanth Ulhas Nair – wrote up a set of suggestions on how one might go about solving the problem of violence against women in India, specifically rape (there have been some horrific occurrences lately in Delhi, Bombay and Bangalore).

Here is one of his suggestions that I particularly liked:

a) In schools, make students do the cleaning and if possible cooking/washing-dishes also. Boys should especially be made to do this. So that they learn to do work which are typically considered to be the job of a woman in India. Moreover this will reduce the class divide in India where there are some ‘inferior/poor’ people who will work for us. Why should there be a mess in schools/colleges? Students should cook their own food and clean their own plates.

But what I really want to talk about today is the counter-suggestion he had made:

The problem with death penalty is that the rapist may end up killing the victim because he feels it will be easier for him to get away with it (since death is anyway the worst penalty he can get, there is more incentive for him to kill her after the rape).

Stricter measures (for example, applying the death penalty to the crime) have been floated around a lot lately, but how do you decide what is an appropriate quantum of punishment?

I am going to see if it is possible to arrive at Nishanth’s conclusion using game theory.

We are going to start with a set of simplified assumptions:

a)  You have two players in this game – the law-enforcer and the law-breaker.

b)  The law-enforcer has two choices – a) to punish the law-breaker with death and b) to punish the law-breaker with a few years in jail.

c)  The law-breaker has two choices – a) to kill witnesses to better his/her chance of not getting caught and b) to not do anything beyond the primary objective of the crime.

d)  The aim of the law might be assumed to be to maximize the number of potential crimes prevented.

e)  The aim of the law-breaker might be assumed to be to minimize the punishment if any that might result from the crime.

The Payoff Function of the Law-Breaker

The law-breaker’s payoff is the punishment, and so is a negative number.

It is set to -6 (maximum punishment) if the law-breaker does not kill the victim after the crime (which could be a burglary or a rape) but the punishment for the crime is the death penalty (to act as a deterrent).

It is only -2 if the law-breaker does not kill the victim, and the punishment is not draconian.

The law-breaker’s payoff is only -3 if (s)he kills the victim assuming the chances of detection decrease by 50% as a result of the murder.

Since the crime is compounded by the killing, the payoff is the same no matter whether the penalty for the original crime is harsh or not.

The Payoff Function of the Law-Enforcer

The law-enforcer’s model is simpler.  It is equal to the number of innocent lives saved.  It is 1 if the victim is not killed.  It is 0 if the victim is killed after the crime.

Analysis

Now to start analyzing the game, you write the assumptions down in a bi-matrix (normal-form game) as follows:

the law (enforcer)
awards a few years in jail
the law (enforcer)
awards the death penalty
the law breaker
chooses not to kill the victim
-2, 1
–61
the law breaker
chooses to kill the victim
-3zero -3, zero
Normal form or payoff matrix of a 2-player, 2-strategy game

The first of the two numbers in the matrix represents the payoff to the law-breaker.

The second of the two numbers in the matrix represents the payoff to the law-enforcer (or society).

Strictly Dominated Strategy

By examining the matrix, it is possible to see that there is no strictly dominated strategy for the law breaker.

A strictly dominated strategy is one that will benefit one of the players more than all his/her other strategies no matter what the other player does.  No strictly dominated strategy exists for the law-breaker in this particular game.

That is because if a draconian punishment strategy is used by the law-enforcer, killing the victim appears to be a better strategy for the law-breaker.  If the death penalty is not used for a lesser crime, then not killing the victim appears to be a better strategy for the law-breaker.

Nash Equilibrium

A Nash Equilibrium consists of a set of strategies for both players that are the best possible for each of the strategies an opponent might choose.

It turns out that this system contains two Nash Equilibrium points.

In this formulation, the strategy pairs that can yield a Nash Equilibrium are:

1)  the law-enforcer does not award the death penalty + the law-breaker does not kill the victim

2)  the law-enforcer awards the death penalty + the law-breaker kills the victim

Conclusion

So, what this analysis suggests is that if the death penalty is awarded for crimes like rape, there will be a strong motive for perpetrators to kill their victims.  Conversely, if the penalty for crimes like rape is less than the penalty for murder, there will be a strong motive for perpetrators not to compound lesser crimes with murder.

What is also interesting to note is that if law-enforcement is not very effective at identifying perpetrators without a victim’s assistance (if there were no DNA matching technology or if the police force were ineffective), a criminal would have a good incentive to kill his/her victims [the result would be obtained if you change the -3 to -1 in the law-breaker’s payoff function].  Ineffectiveness of policing would reduce the negative payoffs for a rob+murder strategy to the point where murder to compound the crime might become an appealing alternative to a law-breaker.

The Alternative Scenario

I had heard from a friend from another country that in his country, thieves would be killed by anyone who caught them (passers by would tie them up and kill them summarily and without trial – by ramming pins into their heads).  I can imagine that this strategy might cause law-breakers to do everything possible to hide the crime – including murdering anyone who might hinder their escape or later identify them to their captors.

So, in a way, the matrix justifies having an effective police force at public expense.

Summary

So, we’ve tried to show using some simple game theory that Nishanth’s intuitions about penalizing rapists with the death penalty are possibly right on target.

However, we have chosen a model that is very simplistic and not a very accurate fit for the problem.  The model chosen is of a static game with complete information, but that is a bit of a simplification.

If you liked this article, you might like some of our earlier writings that attempt to analyze game theoretic models of social media customer service.

Acknowledgement

We learnt a lot about the subject of game theory from a book that is absolutely-required-reading for anyone with the faintest interest in economics and game theory – “Game Theory for Applied Economists” by Robert Gibbons.