Wednesday, May 12, 2010

Ranking and Sorting: two forms of cognition

There are two ways of looking at cognition.
  1. There is cognitivism which looks at the mind as an information-processing system. In this view, it is thinking, i.e. the ability to play with representations of the world inside the mind, that is all-important.
  2. Then there is another view, a heterogeneous set of views that is sometimes called the situated action perspective. Some of the proponents of this view would be Phil Agre, Lucy Suchman, Edwin Hutchins, Rodney Brooks and Eleanor Rosch. In this view, it is action that is all-important. Abstract rule-based thinking is but one, and by no means all-important, resource for action. Equally important are our use of tools and artifacts, and our taken-for-granted bodily and social skills. The situated cognition view locates cognition in our interactions with the world rather than in thinking inside the head. Representations are key but they are by no means solely in the head nor do they mirror the world; rather they are resources for action and are embodied in the tools and artifacts that we use for our tasks.
If you know me (or read this blog), you probably know that I find the situated action perspective far more convincing,. I can't, by any means, give any kind of a logical "proof" for it. But I do think it provides a better description of how we do things in our day-to-day life. E.g. in a form I filled out recently, I was asked to rank a list of 16 items. From a cognitivist perspective, this is a "problem" that is "solved" using utility-maximization; what I hope to do in this post is to show the actual processes that I used to rank the alternatives and also to show that these processes are better described as my interactions with certain external representations of the task. These functioned as tools i.e. resources that helped me complete the task. I also hope to show that by transforming the problem from one representation to another, I could have done the task differently (and more easily).

The housing form is shown above and it asks me rank the 16 types of housing available. Each type, as you can see in the figure, is an ordered pair consisting of a residence hall, and a type of apartment. I was supposed to assign ranks from 1 to 16. I could choose not to rank an option (thereby signifying that I wasn't interested). And I could give multiple options the same rank, if I wished.

From the cognitivist perspective, the process by which I actually ended up ranking these options is not very important. Because at an abstract computational level, my actions can be described as a simple case of utility maximization. I have a certain set of preferences (an upper-limit for the rent I am willing to pay, an interest in living with room-mates rather than alone, etc.). Based on this, whatever I do can be described as calculating a value for each option that measures its suitability for me and then ranking the alternatives based on said values.

But consider what actually happened as I was trying to fill up this form.

It was almost impossible to just straightforwardly rank 16 items without messing up. Some of the problems that I ran into were:
  1. It was impossible to go through the alternatives one by one and assign them a rank. There were two possibilities.
    1. I could go through option 1, give it a rank, go to option 2, and so on. This would only work if I had worked out all the ranks in my head before-hand (impossible) or if I had worked them out on pen-and-paper (which I hadn't).
    2. I could scan all the alternatives, find the one that I liked the most, give it rank 1, then scan all the remaining alternatives, find the one I liked second-best, give it rank 2. This didn't work because (a) I quickly forgot what rank I was on, (b) I had to keep in mind all the others I had previously ranked (or get them by quickly scanning all alternatives) and finally (c) I just didn't know scanning the alternatives which one I preferred.
  2. The form did not give all the information that I thought relevant. E.g. there are 2-bedroom or 3-bedroom apartments in certain residence halls which did not have a living room; I wanted to rank these options lower. Then there were options that I just did not prefer i.e. I had a "black-list." I had to flip back-and-forth between this page and the pages describing the apartments in detail so that I would not accidentally rank something in my black-list.
In a sense, the problem was this: not only was I trying to rank all the alternatives, I was also evaluating the criteria I was using to do so at the same time. That is, I was creating the "rules" that I would use to prefer one alternative to another in the process of applying them to specific alternatives! Note however that the representation that I had been given to work with -- a list of alternatives along with the possibility of assigning a number i.e. the rank to each -- was not very conducive to what I was doing.

Ultimately I ended up following the strategies below:
  1. I first determined a rough order of preference in my mind. E.g. (1) efficiency apartments, (2) 2-bedrooms, (3) 3-bedrooms, (4) 4-bedrooms, and (5) 1-bedrooms. Of course, this wasn't the whole story since there were many exceptions (the black-list) to this preference. But as a rough guess, it was accurate.
  2. Then I went through the options one-by-one keeping the above list in mind.
    1. So I first went through all the efficiency apartments (there were 4), looked at their particulars (their price, whether they were on my black-list, etc.) and ranked them. If one was in my black-list, I chose not to give it a ranking.
    2. Then I went through the 2-bedroom apartments and did the same. I had to keep the last ranking I had assigned in mind. E.g. if I had ranked the efficiency apartments from 1 to 3 (not ranking the one in my black-list), then I had to remember to rank the 2-bedrooms starting with the rank 4. It was crucial to remember this. Because if I forgot, I had to scan the whole list again for the last ranking so far and this was not a fun task. If I mis-remembered, then I would mess up all subsequent rankings. I could have chosen to write this last ranking down to avoid this.
    3. And then I had to do the same for all the other types of apartments: 3-bedrooms, 4-bedrooms and 1-bedrooms.
    4. One of the reasons why I could do this was because there were no "anomalies" in my choices. E.g. there was no stray 3-bedroom that I preferred to a 2-bedroom. Had that been the case, I would have had to adopt a slightly different strategy. As I was ranking the 2-bedrooms, I would have had to look at the 3-bedrooms as well. And I would have had to look at the 3 and 4-bedrooms together. And so on.
  3. Once all this was done, I went back to all the alternatives I had not ranked (because they were on my black-list). I had the choice of not ranking them or giving them the last few ranks. Again it was crucial for me to remember the last rank that I had assigned. E.g. if the last ranking was 13, and I had 3 more left, I would assign them to ranks 14, 15 and 16.
Remember that this is a gloss on how I did the task. A narrative that I have constructed by looking back on what I did and trying to be conscious of what I was doing when I did it. It should, by no means, be considered a true account of what I did.

But that said, let's look at this account and see whether it can be reasonably described in terms of rule-following or utility-maximization. The answer is clearly, at some level, yes. But consider the following points:
  1. While I did follow a rule (a "heuristic"), at no point did I assign any value for each alternative. Nor did I ever consider all the alternatives together.
  2. Instead I used one of my selection criteria to break down the 16 alternatives into 5 groups in decreasing order of preference (efficiencies, 2, 3, 4 and 1-bedrooms). Then I ranked the items in each group. This was far easier to do since each group had only 4 or 5 members.
  3. A lot of what I did was, in effect, my way of interacting with the available representation of the problem (in this case, a list whose items could be assigned ranks).
Now consider how much more simple the problem would have been if I had an interface that allowed me to sort the table, rather than rank it, using mechanisms like drag-and-drop.


Or suppose I had made written each alternative on a piece of paper, and then sorted the pieces into a list with my most preferred alternative at the top and the least-preferred one at the bottom. Like so.


This makes the task so much simpler, no?

In effect, this is a transformation of the task: from a ranking task to a sorting task. Computationally, the "problem" remains the same, but this transformation makes it easier to solve. Here is why sorting is easier than ranking:
  1. Sorting allows us to focus on a subset of the alternatives without being distracted by the others . E.g. I can focus on whether I prefer an Edgerton 1-bedroom or a Tang 3-bedroom by moving the representations of these alternatives close together and moving all the rest out of my field of vision. This is impossible to do in a static list whose items need to be assigned ranks.
  2. Sorting converts the ranking problem into an ordering problem. E.g. once I have arranged alternatives A, B, C in that order and I decide that I prefer C to B, all I need to do is insert C between A and B. The order changes immediately to A, C, B. If I was assigning numbers to A, B and C this same step would involve me having to change the ranks of each one of them.
  3. Sorting eliminates any need for memory -- which is the hardest for the mind to do without external representations. E.g. one does not have to remember, say, the last rank that one assigned; instead the representation will itself tell us what the current state of the matter is.
What I write here has similarities both to the distributed cognition hypothesis and the extended mind hypothesis.

Selected References
  1. Edwin Hutchins, Cognition in the Wild, New edition. (The MIT Press, 1996).
  2. Abigail J. Sellen and Richard H. R. Harper, The Myth of the Paperless Office, 1st ed. (The MIT Press, 2001).
  3. David Chalmers and Andy Clark, “The Extended Mind,” Analysis 58 (1998): 10-23.

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