basics: conceptual triangles

Sometimes, we have to think in triangles.

In the transit world, for example, we know that ridership arises from a relationship between urban form (including density and walkability) and the quantity of service provided.  For example, if we focus on local-stop transit, the triangle looks like this:


You can think of development and service as inputs, and ridership as the output, but you can rotate the triangle any way you like.  For example, if you want to justify an increase in service, you want both some existing ridership success and also evidence, from the development density, that there’s more potential.  In other worse you want to say “Ridership + Development –> Service”  On the other hand, if you want dense development as an output, you want a transit line that feels permanent.  That’s going to be one that already has high service, achieving high ridership. “Service + Ridership –> Development.”  (In each case, the right-arrow means “supports” or “helps to generate” or “is one of the crucial necessary conditions for”)

I am reminded of this triangle because transit discussions are full of assertions about the relationship of two points on this triangle.  Some of these are quite famous.  Pushkarev and Zupan, for example, are dutifully cited in every article that deals with this topic.  WIth a publication date of 1977, they are one of the oldest must-cite authorities in transit research; it’s as though they’ve passed over into the realm of scripture.   Their conclusion?  “A net residential density of 15 units/acre supports a service level of 10 minutes or better over a 20-hour span.”  This is a stated relationship between two of the three points on this triangle, service and development, without reference to the third, ridership.  So hidden inside the verb “supports” is an assumption about what level of ridership is acceptable.

There is, to my knowledge, no agreed standard about what level of ridership is acceptable, nor should there be.  Every city or agency decides that for themselves.  That means that logically there can be no answer to the question “is development pattern and density x sufficient to suppoert service level y?”

In the British-influenced world, of course, there’s often a hidden implication that the ridership standard should be “profitability.”  Certainly, if that’s your goal, then you’ve fixed that variable and can now look more coherently at the relationship between the other two; in other words, it then becomes coherent to ask “what service level should be offered in response to each development type, so as to hit a goal of profitability.”  (Yes, fare policy plays a part, and that’s still another variable, but you can also choose to hold that constant.)

But of course, most of us don’t think transit should aim for profitability.  A profitability paradigm assumes that government has no public interest in the success or failure of transit, just as it has no interest in the success or failure of Coke Zero.  And obviously that’s wrong.

So when I hear people either quote or update Pushkarev and Zupan, saying that density x supports what level of service y, I hear pure incoherence.  The statement says nothing that’s useful to me.  What am I missing?

UPDATE:  Jeffrey Zupan himself wants to assure us that his work was based on a clear ridership assumption, expressed in the form of targets for cost/passenger and cost per passenger mile.  Unfortunately, most people who quote his work forget that part.  In doing that, they’re implying that the ridership target that Pusharev and Zupan chose is the right one for their own community, even though they don’t know what it is!

9 Responses to basics: conceptual triangles

  1. Cap'n Transit January 23, 2011 at 2:23 pm #

    Well, one thing you (and everyone who believes that Pushkarev and Zupan formula, which in turn relies on Simpson and Curtin 1968) are missing is that transit ridership is dependent on the relative attractiveness of alternatives, as observed by Kemp (1973). He writes:

    One might hypothesize that, given the initial decision to travel, transit riding will be higher when the relative prices of substitute modes are at their highest; and that under such conditions transit fare elasticities will be relatively low. It follows that one would expect … fare elasticities to be relatively low in very large cities with highly congested central areas, particularly for those modes catering to long-haul commuter traffic.

    I have a copy of Kemp’s paper in PDF format; let me know if anyone wants a copy.
    I would urge everyone to ask themselves, if profitability is not the goal, what is it? My goal is to get people out of their cars, so that we can reduce pollution and carnage, and improve efficiency and social relations. If you’re a transit planner, maybe your goal is to make your agency head look good so that you get promoted. Would a defeat for a competing road ultimately help those goals?

  2. Jarrett at January 23, 2011 at 2:25 pm #

    Cap'n.  You betcha.  That's another dimension.

  3. Cap'n Transit January 23, 2011 at 3:21 pm #

    Actually, I don’t think you need another dimension. You just need to be neutral as to which direction you’re going in, as I was with my original cycle diagram.
    Government priorities can favor roads or transit, which makes them more or less desirable relative to each other, and that influences people’s choices, which in turn determines ridership (and AADT), and that influences government priorities, which brings us back to the beginning of the cycle.

  4. Rob January 23, 2011 at 3:57 pm #

    Jarrett, do you think there is really an equal two-way relationship between each of the three factors in your diagram? That could suggest to transit decision-makers that it’s reasonable to deploy unproductive service in hopes that it will create development. Some decision-makers believe that already, but there’s not a lot of evidence I’ve seen that adding transit in low density areas affects development at all (though significant transit capital facilities can probably have an influence on the speed of development that is already likely to occur). What *is* affected is the amount of funding left available for service in places where there is real demand. So I don’t think it’s quite right to show equal two-way arrows as if each factor can have an equal effect on the equilibrium without affecting efficiency.
    There are certainly a lot of other factors aside from development and service that result in demand, including demographics, pedestrian accessibility, and some consideration of where the service goes and how fast it gets there. There have also been systemic changes that have occurred in America since the 1970’s that affect transit demand. But I think it’s fair to suggest that demand can be calculated, and that it’s reasonable to define service levels based on that calculation and fine tune based on ridership.
    The bigger question I think you’re asking is how to determine the right level of service – and I think that points to your budget line. Whatever your budget, you’re going to want to distribute service in proportion to the amount demanded, but if your budget line is higher, then it’s possible to expect a higher level of service associated with the factors that determine demand.

  5. Jarrett at January 23, 2011 at 5:10 pm #

    Rob.  Good question.
    I guess I'd say that the triangle means "if you have two of these, you have some reason to hope for the third, though other dimensions, like the cost of driving, investment climate, etc will of course play a role."

  6. Danny January 23, 2011 at 8:16 pm #

    I know people like to laugh about the Adam Smith’s invisible hand concept, no doubt because it has been both hammered to death and touted from on high by people who misunderstand it for two centuries now. But at least in this situation, it most definitely applies. The quest for profit most definitely can result in strong social positives, in many cases it can do so much better than an entity disinterested in profits.
    The trick here is that high ridership directly correlates with high revenues and lower costs. Think about the general social goals of public transportation: increased health and safety, lower total resource consumption, better economic efficiency, etc. All of these benefits become better with higher ridership and lower costs.
    Generally speaking, the criticisms of the profit-seeking model are complete red-herrings…often misunderstandings extrapolated from completely different business types. For example, the idea that profit-seeking transit operators would just jack up prices…that might be the response of a profit-seeking telecom in the 1980s, but not a profit-seeking transit operator. At least not the intelligent type. The rules of competition demand differentiation, and higher price points in an environment competing with well entrenched automobiles would make any sort of increase in pricing an absolute disaster for demand. Besides, the competitive strength of transit is serving high volumes, not premium qualities…and intelligent businessmen tend to follow best practices like “leveraging your strengths”.
    At best, there is only one incentive of profit-seeking transit operators that doesn’t perfectly align with the commonly cited social goals of public transportation: Service levels. Notice I said “doesn’t perfectly align”…because for the most part they do align pretty well. If transit service is operationally profitable, you make more profits by offering more service. The reason that they don’t perfectly align is when some lines are not profitable, their incentive is to cut service levels. A non-profit agency would be more likely to cross-subsidize.
    But then again, transit agencies that aren’t motivated by profits haven’t proven to be angels in that regard either. Rent seeking, political pandering and tampering, and special interest proliferation have all plagued municipal transit agencies across the country. Our world’s recent experience with communism shows that eliminating the motive for organizational profits does not eliminate the motive for individual profits, ie rent-seeking. We shouldn’t be so naive to assume that profits are the only evil we should worry about with transit operation. In the case of transit, we should be happy about high ridership, and sometimes just accept that profits are the small price we pay for it.

  7. K January 23, 2011 at 11:42 pm #

    Maybe the regurgitation of the Pushkarev and Zupan mantra is nothing to do with transit per se but is indicative of something deeper. I think it is a working example of the “target” accuracy versus precision analogy.
    A statement like “a net residential density of 15 units/acre supports a service level of 10 minutes or better over a 20-hour span” implies precision, even if the numbers being used in this instance are fairly round. Work has obviously gone into the calculation. That’s not to say it is accurate though.

  8. Tom West January 24, 2011 at 6:45 am #

    “So when I here people either quote or update Pushkarev and Zupan, saying that density x supports what level of service y, I hear pure incoherence. The statement says nothing that’s useful to me. What am I missing?”
    The missing thing here is that ridership is not purely a function of development density and service levels. Fares, journey times (relative to cars), relability, and comfort within the bus are all things that obviously effect ridership. However, there is more… transit agebncies can also increase ridership without changing the actual service in any way whatsover, through things like advertising, information provision, or even personalised travel planning.
    Where I live, there isa wide range of densities, and I often hear transit agencies saying that lower desnity areas will *always* have their current low level of service. This seems a very fatalistic attitude to me, and has it may have its roots in statements like Pushkarev and Zupan’s. I think it more accurate to say that lower densities/service levels require more effort to obtain a given level of ridership.

  9. Eric Doherty January 24, 2011 at 10:17 am #

    Jarrett, you have hit the nail on the head. The numeric rules for transit and density are incoherent because they are based on the idea that density is THE dominant factor.
    In Metro Vancouver (Canada), the relative attractiveness of alternatives seems to have far more to do with mode choice than density. We have some significant high density nodes where transit service is very poor and access to the freeway network is good, and transit ridership is therefore low.
    In Ottawa, if I get my information right, there are low density suburban areas with direct bus service to the downtown core that have remarkably high transit ridership. It seems that the deliberate policy of making parking expensive downtown is a big part of this success.
    Density is an important factor, but it is only one factor among many (including road building, parking policies and transit fares).