In want of importance

The second weekend of October, I attended the 50-year anniversary of my student guild at the university. With one thousand guests present, I met a lot of old acquaintances and saw many people I had never seen before, the eldest having started their studies over fifty years ago. In the discussions with closer friends and more distant ones two things caught my attention:

  1. Understanding what everyone does in their daily work seemed quite difficult.
  2. In describing what they do, professionally and in their free time, people seemed to be very competitive.

When describing my current life and professional pursuits to others I tried to give a short and very tangible description, something like: “I work in strategic procurement, buying R&D services from external engineering companies. Among other things I look for suitable providers and negotiate and close the contracts with them.” I don’t recall mentioning my title even once, since “Project Manager” hardly tells anyone, what I do.

When asking others what they do, the answers were, to tell the truth, difficult to understand and memorize. Should I be asked now to repeat those descriptions, I might recall, very vaguely, a few of the maybe ten occupations and task descriptions I heard during the party. I remember someone mentioning: “I work a lot with Excel tables”, which was easy enough to understand. And I would bet, that the majority of us work with Excel tables and PowerPoint presentations, either creating them, seeing them presented or both. But those two are just tools, so the exact content behind the work does not become any clearer. So the main question, based on my two observations is, whether work is that complicated or whether we just want to make it look like that.

It’s complicated, it’s important and so am I

My conclusion, after some pondering, was that today’s work, having become increasingly specialized, is difficult to be described to or be understood by an outsider, even if they work in a neighboring field or have similar education. Another factor might be, relating to my observation number two, that we want to give a polished picture of ourselves, seeming to be more successful and important than we really are. After all, everybody wants to feel important.

A further thought on my observation number two was, how intentional this competitiveness and bragging might be? In the discussions at the party, I tried to avoid exaggerating my current job or personal life. But if many people appear to me as bragging when telling about their lives and jobs, is it just my observation, are they doing it unintentionally or are they really trying to show off?

If it’s just my observation, than maybe I am feeling inferior or jealous because my job or life does not feel that important in comparison to theirs. If people are bragging, they might be doing it unintentionally, which is actually again more dependent on the listener’s subjective view. However, if people are really bragging, omitting here the question of how to measure “real, intentional bragging”, they might be feeling inferior or feel the need to underline their own importance. In each case, the question is, whether the parties in conversation perceive themselves as “equally important”, and consequently adjust their wordings and interpretation of the spoken words.

I suppose the essential message here is that bragging is very subjective and situation dependent, and that work has not really become that complicated although tasks have become more specialized. While more specialized, each task is also limited in scope and therefore not necessarily complicated, but just not readily accessible to others who are not familiar with the very field. However, each or most of the tasks and jobs would still be understandable and accessible to many people, had they just chosen to engage that very field. It’s our need to feel ourselves important that makes us overcomplicate things when describing our lives and achievements.

Many of us, me included, live our lives with daily routines. These routines might sound boring to someone, but if I enjoy them and want to adhere to them, as I mostly do, I should not be ashamed to tell about my life without any grandiose vacuities.

Backward induction in procurement and mechanism design

About a month ago, I delivered my colleagues a training on backward induction, a method used in game theory to find Nash Equilibria in games that have pre-defined end points. I used materials and examples from the Open Yale course on game theory, since they were illustrative and easy to understand.

After the training, we had some discussion on when one can use backward induction, especially in real life, where we often have open-ended games. During the discussion, I was not able to provide any good example on when to use backward induction, but afterwards a great example came to my mind. Not surprisingly, this example was mechanism design.

Mechanism design is a sub-field of game theory focused on the study of creating and implementing mechanisms and incentives that align the interests of multiple agents. Earlier this year we had an external training on auction design, an application of mechanism design, where the goal is to design such an auction, that the buyer gets the best product for the lowest price. Obviously, auction design can be a powerful tool for any procurement professionals. Using auction design as an example of mechanism design, I will list some delimitations and pre-conditions for backward induction.

Backward induction in business transactions and relationships

Game theory and backward induction can be used in procurement to anticipate potential proposals and prepare counter-proposals, or prepare proposals to direct and distract the other party. Since a negotiation does not necessarily have a clear end from the start, using backward induction extensively can be very difficult, since the potential branches in the decision tree are not limited.

Another aspect in using backward induction is that all parties must be “playing the same game”. For example, if you are concentrated on the immediate outcome of the negotiation, while your opponent is looking at the long-term relationship between your companies, you might be going through very different decision trees with differing optimal outcomes for the immediate outcome. In addition, if the other party does not use backward induction but rather shoots from the hip, you cannot directly expect them to do choose optimally.

In procurement, our job is to create markets and create competition to leverage the market mechanism in buying the best quality we need for a good price. Therefore, mechanism design and game theory can be used to create such a game, a market, where the value to us can be maximized. The idea is to create an auction, where, using backward induction, the interests of the bidders and the buyer are aligned in such a way, that the buyer’s utility is maximized in the auction. Here it is important to make sure, that all the bidders are “playing the same game” and are deducing their actions backwards from the pre-defined end.

There is extensive research on auction and mechanism design. When we have set up the optimal auction design, we face another game, a meta-game, where we have to convince potential suppliers to participate in the bidding or auction, convince them that we are good customers and worth their business. Here we are again playing a long-term game without a pre-defined end, where the parties must convince each other of the benefits of doing business with each other and deliver on that promise. This relationship might also be the corresponding might also be aligned using mechanism design, but due to the scope it is a much more difficult task than a single auction.

Learning MATLAB

Continuing my apparent hobby of taking up and passing MOOC courses, I finished yet another Coursera course end of September. It was an introductory course on programming using MATLAB from the Vanderbilt University. The course lasted nine weeks and included the basic functions of MATLAB, to which we got introduced by following the weekly lectures and doing the homework.

The weekly video lectures were very good, containing clear introduction and guidance on many useful MATLAB functions and their syntax. The weekly exercises had a lot of variation and required some own studying to come up with novel solutions and learning about function that were not always covered by the lectures. Some exercises were also adapted physics problems, which gave a first view on how MATLAB can be used in physics.

I can highly recommend this course to anyone who is interested in learning programming but already has some basic knowledge on the topic. I would not recommend this course to anyone without any prior experience in programming, but programming experience is not a course requirement per se. MATLAB’s focus on using matrices to solve problems is likely to appeal to those inclined to physics or engineering sciences, where linear algebra is used to solve many problems. The brief introduction on using MATLAB to manipulate Excel files might be interesting to many of us who are used to using PivotTables but have had many troubles with Excel, when it comes to doing matrix manipulations.

Biased merit and diversity

In two earlier posts I discussed the roles of skill and luck in being successful and getting rewarded. Recently I read a Harvard Business Review* (HBR) article on the topic and wanted to get briefly back to this important topic.

As the fashion goes today, diversity is the hot topic on improving performance in organizations and promoting equality.  At the same time organizations face the problem of increasing diversity in the correct and effective way. This starts with the definition of diversity. The HBR article mentions that Millennials see diversity as “valuing ope participation by employees with different perspectives and personalities”, while older generations see diversity as “equitable representation and assimilation of people from different demographic groups”.

Even if we manage to agree on whether to promote diversity of thought and personalities, different demographic groups or still something else, choosing the right people is still a challenge. An obvious answer is to use merit based assessments. Yet, even then we face problems, since, it turns out, the very definition of merit depends on the person being evaluated.

The HBR article cites a study, where a consulting firm’s recruiting process was observed to see how merit is defined. It became clear that merit is not a fixed personality attribute or a specific behavioral model for a specific situation. When the consulting firm had interviewed job candidates and the interviewers came together to discuss their observations, they ended up trying to reach consensus on the maybe-maybe not candidates; the clear no-gos and top performers were not discussed. When discussing the still open cases, a person’s evaluation was highly influenced by his racial background: “For example, black and Hispanic men were often seen as lacking polish [, meaning communication skills,] and moved to the reject pile, even when they were strong in other areas, whereas white men who lacked polish were deemed coachable and keep in the running.”

The italics in the above passage are mine, since the word coachable really caught my attention here. The passage says that black an Hispanic men lacking polish were perceived to have incomplete skill sets, maybe without improvement potential, while white men with similar skill sets were seen amenable to coaching, something that might be even desirable to educate a new employee into the company culture.

In another passage from the article the difference in social behavior were discussed: “Nonwhite were rejected for being unassertive, but in white, modesty was seen as a virtue.” Here, like with the lack of polish, we see how some candidates missing a character are taken to be incomplete and also lack the potential for further development, while other candidates with lacking skill sets are seen as fertile ground for education and personal development.

Quite obviously merit based evaluation and remuneration is not a panacea, all the more if we have no clear, for all equal definition of merit in a given situation. Thus, we should be aware and acknowledge that our very definition of merit can be biased. Acknowledging this fact is one step closer to doing fair, merit based evaluations and promoting diversity based on true, equally assessed merit.

*Harvard Business Review July-August 2016: We Just Can’t Handle Diversity

Edit: Corrected typos on 26.3.2017

Functions and mental health

Going through my old university mathematics book (ISBN 952-91-9157-X), I read a chapter introducing and discussing functions. At the end of the chapter (see page 163), I saw an interesting exercise that took an interesting perspective on using functions to think about relations between everyday things.

I first introduce a definition of a function, adapted from the book, and then the mentioned exercise, also from the book.

A definition of a function:
A function is a triple (set A, rule f, set B). This means that we have a rule f that pairs each member of set A with exactly one member of set B.

This “pairing” (or mapping) is written as y = f(x), y B for every x A. We might also write f: A → B which means that rule f maps set A, f’s domain, to B.

As we can see from the definition, pairing multiple, different members of set A to set B is not precluded, but each member of A is paired with one and only one member of set B. In addition, it may be that not all members of set B have a pair in set A. I’ll now turn to the exercise.

Psychiatrist’s reception as a function

A psychiatrist’s reception can be modeled as a triplet (psychiatrist, patient, diagnosis). Under which assumptions are the following cases functions?

a) psychiatrist: patients →  diagnoses
b) patient: psychiatrists   diagnoses
c) psychiatrist: diagnoses   patients
d) patient: diagnosis   psychiatrists

We we’ll examine each case from a) to d) individually. In general, based on the notation introduced with the definition of a function, each of cases a) to d) have the following form:

rule: Set A →  Set B

Our chosen triplet (psychiatrist, patient, diagnosis) has to be quite restricted, if cases a) to d) are to be functions. First, a psychiatrist is not allowed to change his diagnosis for a specific patient, since this would preclude mapping the respective members of Set A each to a single member of Set B, as we we’ll soon see. In addition, Set A has to be quite restricted, if all its members are to be mapped. We therefore have one assumption that pertains to all cases a) to d):

Assumption 1 (A1):
A psychiatrist cannot change his diagnosis for a specific patient.

and another assumption whose exact form depends in the respective case:

Assumption 2x (A2x, where x = some case a)-d)):
Set A is limited so that each of its member is mapped to Set B.

Cases a) to d) as functions

Starting with case a), a psychiatrist maps every patient to a diagnosis, potentially multiple patients to the same diagnosis. Assumption A2a) limits the set of patients to those patients that the psychiatrist has diagnosed. The psychiatrist has given every patient some diagnosis, potentially the same to each one.

In case b), a patient maps every psychiatrist to a diagnosis, potentially multiple psychiatrists to the same diagnosis. Assumption A2b) limits the set of psychiatrists to those that have diagnosed the patient. Each psychiatrist may have given the patient the same diagnosis, but not necessarily.

In case c), a psychiatrist maps every diagnosis to a patient, potentially multiple diagnoses to the same patient. Assumption A2c) limits the set of diagnoses to those that the psychiatrist has given to some patient. Each diagnosis may have been given to the same patient, but not necessarily.

In case d), a patient maps every diagnosis to a psychiatrist, potentially multiple diagnoses to the same psychiatrist. Assumption A2d) limits the set of diagnoses to those that the patient has received from some psychiatrist. Each diagnosis may have been given by the same psychiatrist, but not necessarily.

As we can see from the cases above, a large (> 1 member) Set A may give us some interesting real-life consequences in each case:

  • In case a) the psychiatrist may give each patient the same diagnosis.
  • In case b) multiple psychiatrists may all give distinct diagnoses to the same patient.
  • In case c) the psychiatrist may give multiple diagnoses to the same patient.
  • In case d) a patient may receive multiple diagnoses from multiple psychiatrists or from just one.

Now we have defined, under which assumption cases a) to d) are functions. At the same time, we see that these assumptions are not enough to guarantee that our functions correspond to real life. For our function to correspond to real life, we would intuitively like the following conditions to be true:

  • A single patient gets a single, unchanged diagnosis from a single psychiatrist on each visit on the short term. (C1)
  • A single patient gets the same (or almost the same) diagnosis from different psychiatrists on the short term. (C2)
  • A psychiatrist’s diagnosis may change on the long term. (C3)
  • A change in a psychiatrist’s diagnosis can be very dramatic compared to the previous diagnosis. (C4)
  • Similar patients get similar diagnoses. (C5)

A more realistic function

As we saw in the analysis before we have two assumptions that define whether cases a) to d) are functions. Assumption 2 cannot be said to be either realistic or unrealistic, since we only define Set A, which is just an arbitrary choice. Assumption 2 merely limits the usage and potential scope of our function: the more limited our Set A, the fewer are the situations where the respective case is a function.

Assumption 1, however, can be evaluated to be more or less realistic. A psychiatrist changing his diagnosis over time is not something we can define, rather it is a given that is either true or false: between now and a given point of time in the future a psychiatrist either has or hasn’t changed his diagnosis of a patient.

We see that A1 can be evaluated as being realistic or not, depending or whether we are considering a shorter or a longer period in time. On the short term it sounds reasonable to assume that a psychiatrist’s diagnose of a single patient does not change (C1), while on the long term we might assume some changes (C3), especially if the patient has some mental condition. Even for currently mentally healthy people A1 is not necessarily true in the long term, since a person might develop a mental disorder (C4). However, we can overcome the long-term limitation of A1 by creating a composite function for the long-term perspective (C3). This function consists of the respective short-term functions, whose time horizons do not overlap but form a continuum. Thus, this long-term function allows a psychiatrist to change his diagnosis of a patient over time, but for shorter periods, the diagnosis stays unchanged.

By introducing time as a further variable we have redefined our triplet (psychiatrist, patient, diagnosis) as a new triplet (psychiatrist, patient, diagnosis(time)), where the diagnosis is a function of time. By defining psychiatrist = psychiatrist(i) where i is the index of the respective psychiatrist we also introduce C1 into our triplet, thus creating a triplet (psychiatrist(i), patient, diagnosis(time)). In order to consider C5, we also adjust our original triplet in such a way. that each patient is also a function of his attributes that define his mental health, which then influence the respective diagnosis.

Taking case a) now as an example for using the new triplet we observe case a)*:

a)* Psychiatrist(i): patients(attributes)  diagnoses(time)

In case a)* a psychiatrist gives each of his patients always the same diagnosis on the short term, but is allowed to give a different diagnosis on the long term. Previously we defined that the diagnosis remains unchanged on the “short term” but did not define short term. In fact, we could define our time intervals to be infinitesimally short. In this case, the psychiatrist would be allowed to change his diagnosis as quickly as he can, but this is hardly reasonable. As a gut feeling, I would say that our time interval, during which the diagnosis has to stay the same, could be anything between months and years, depending on the patient. Thus, we run into quite subtle questions when deciding, whether we have defined a function or not. Additionally, we would have “patient” as a variable when defining the time interval, thus ending up with diagnosis = diagnosis(time(patient)), making our function even more complicated. Actually, a more clear notation for our new function would be

a)*’ Time: Attributes (Psychiatrist(i): patients(attributes) → diagnoses)

Now a given point in time defines which attributes belong to a specific patient. Then this patient receives from a psychiatrist a specific, unchanged diagnosis within the defined time period, and patients with similar attributes receive the same diagnosis. This seems more like what we would expect to see in real life.

I conclude by saying that case a)* also allows a patient to get different diagnoses from different psychiatrists. For C2 to hold we must also require that the difference between the diagnoses provided by two different psychiatrists is always “small” enough. Here “small” means, roughly speaking, that each psychiatrist could agree on the main points of the other’s diagnosis, while they might have a difference of opinion on some details.

Final thoughts

I was thinking about writing just a few chapters on this but it turned out a bit longer, and I could have written even more. This whole exercise got me thinking more about what function are and how we define them. Especially the properties of nested function like diagnosis = diagnosis(time) and patient = patient(attributes) awoke my interest, since they show how careful we have to be when defining mappings and boundary conditions for them when modeling the real world. It is also clear that at some point we have to make simplifications, if we want to have a usable model and avoid getting entangled in endless nested functions.

I would say that case a*’) as a function captures quite well the essence of psychiatrist’s reception, while also considering potentially multiple psychiatrists, patient attributes and temporal changes in these attributes. The model is surely not perfect, but to me it’s a good start.