All you need is friends, a view and some good cognac

Here a couple of pictures I have been meaning to post for a while now. In the summer of 2013 two friends visited me while I was writing my master’s thesis in Switzerland. We did a trip to central Switzerland including some light hiking. Before departing we bought a small bottle of cognac by the liter at a small store in Zürich’s old town to be consumed on a good spot.

Below you see one of my friends and me sitting and enjoying the view. The bottle is not in sight, but it is there somewhere, maybe between us. My other friend was the camera man. A big thank-you to both of them; it was a great trip with good experiences and memories, including Lars the llama, a very fatty Swiss sausage and disproportionate salad portions at the university cafeteria.

The philosophers
The philosophers
The travelers
The travelers

Leubergcup 2016

As previously mentioned, I will be posting some pictures from our competitions this season. Last Saturday we participated in Leubergcup in Zuwil. We did quite ok, placing 4th out of 11 in gymnastic, 6th out of 13 in flying rings and 12th out of 20 teams in 80 m relay We can still improve next weekend in Gampel and am sure that we wild, now that we have the first competition of the season behind us and have gotten in the groove.

Unfortunately the pictures I took with my mobile phone were quite bad so I’ll be adding links to photographs taken by my friends, as soon as the pictures are uploaded on our sports club’s website. Anyway, here two pictures taken by me to give you an idea of the event. I especially like the tradition of bringing the club flags to the event and having them present, whenever a club’s team is completing an event. It gives a nice touch of dignity to the whole event that in itself is very relaxed though competitive.

Flags at Leubergcup 2016
Flags at Leubergcup 2016
Flying rings at Leubergcup 2016
Flying rings at Leubergcup 2016

 

 

 

 

 

Edited on 29.5.2016: Added link to the photos on our sports club’s website.

Starting the competition season

The season for the country-wide competitions on gymnastics, track and field and some other sports is nearing. During the next five weeks, larger and smaller competitions will take place all over the country, the largest ones bringing in thousands of people to small villages to compete, follow the competition and spend warm summer days in good company. Our sports association will be taking part in three competitions: Leubergcup next weekend in Zuwil, Oberwalliser Turfiest in Gampel the weekend after that. For us the season will reach its high point in Rheintaler Turnfest mid-June in Gams.

Last year our sports association was awarded at the Leubergcup for participating in each of the 25 annual competitions having taken place that far, and this year we are the 26th time there. I will be taking some photos and will upload them to the blog for some impressions. I am hoping for good weather and counting on good performance and lots of fun.

Beauty of nature

Just about a week ago, the first full week of May, I had a long weekend, during which I made some hikes to the nearby forests and hills. Below are some photographs from those trips, showing calm forest views and mighty mountain peaks glimmering in the sun. A big thank-you to my mother for her great company and for these great pictures.

Geissbach
Geissbach
Geissbach
Geissbach
Margelchopf
Margelchopf

Reducing car traffic – a game theoretic view

Last week I wrote about the Slow-up event and the question of reducing car traffic. I also mentioned that reducing traffic is a question of incentives.

In Switzerland, the citizens will be voting on June 5th over a motion to direct the currently collected taxes on fuel in full to the upkeep of the road network. As in many EU countries, the different taxes, including a mineral oil tax or an excise duty and the value-added-tax, the total price of fuel in Switzerland contains over 50% taxes.

The motion argues that by directing the collected fuel taxes to the upkeep of the road network clear benefits will be gained:

  • streets will become safer in the living areas as heavy traffic is rerouted to new routes avoiding these areas
  • traffic jams can be reduced by building more capacity. This will also reduce the costs of lost time spent in traffic jams.

Both listed benefits focus on the aspect of added capacity, since adding capacity supposedly directs traffic outside of living areas and also reduces traffic congestion.

Added capacity does not necessarily reduce traffic jams but adds throughput

At first the adding of capacity seems like an intuitive answer to rerouting traffic and reducing traffic jams, but a game theoretic analysis shows this is not necessarily the case.

With an existing capacity of the traffic network an individual person has the choice of using his own car, taking public transport or postponing (or even cancelling) his trip. As long as the time TC by own car is the same or lower as the time TB used by taking public transport, the individual will take his own car. Also, when the traffic starts jamming (or the person expects traffic jams), he will postpone or even cancel his trip, if the value T of the time lost in the traffic jam is higher than the gained benefit B of making the trip. As the traffic consists of multiple individuals making these evaluations, the amount A of traffic on the streets is limited by inequalities TC < TB and T < B. As long as these two inequalities hold, more people will be taking their own car and will be making their trips, instead of postponing or cancelling them. On balance people are indifferent between their options, each according to their individual valuations.

I am assuming here that most people have roughly the similar values of TC, TB, T and B: since most people are “ordinary” (in the central portion of the bell-curve) in many aspects, it is reasonable to assume that they value their time quite similarly. This means that while an individual person might choose co postpone his trip. because the traffic network is already full, he might do the same try another day, thus “forcing” another person with the same values of T and B to abstain from traveling that day. It is worth mentioning that some individuals with extremely high values of B might never end up postponing their trip.

Now, let’s observe what will happen, when the capacity of the road network is increased to C2 > C. It immediately follows that the travel time, whether by own car or by public transport is lowered, since there is more space for the current amount of traffic A. Also, taking own car becomes more profitable and the inequality TC < TB will hold , since the public transport is always slowed down by its fixed routes and required stops. Since the use of own car becomes more profitable and the value of making the trip exceeds the value of postponing or cancelling it, more trips will be made by own car and the total amount of trips made will increase. This increase will continue, until the inequalities TC < TC and T < B no longer hold, at which point people as a whole are again indifferent between their respective choices.

Now we have a larger amount of traffic A2 > A (i.e. vehicles on the road) than before and people are using the same amount of time for their travel, since the increase in traffic takes place at the margin (T <  B and TC < TB) where we have a lot of people with similar preferences. When, for some people, TB > TC and T < B, they take public transport, so the increased capacity contributes to the use of own car and the total amount of people traveling. The increase in road capacity did not reduce the congestion or travel times, but just increased the use of own car and the number of trips made.

Changing the payoffs changes traffic

We observed that with added capacity of the road network, people will increase the use of own car and will complete their trips as long as TC < TB and T < B. This observation directly points out, that changing behavior requires changing people’s payoffs. It is also necessary to be careful about, whose payoffs should be changed, to have the desired effect. To observe a change in a person’s equilibrium strategy-mix, the payoff’s of others must to have changed, so that the first person is again indifferent between his choices in the new equilibrium. If, as the mentioned motion suggests, traffic is to be reduced, each individual person would be traveling less on average in equilibrium. It then follows that the benefits of traveling in relation to its costs would have to be lower than initially.

A strategy-mix can be interpreted as:

  • the probability of a single person choosing a specific pure strategy
  • a person’s expectations towards the other players’ choosing a specific pure strategy
  • a portion of players playing a specific pure strategy.

In the case of traffic jams, the first and third interpretation are the most obvious ones. We would a observe a person traveling less, when all other people were indifferent between traveling or postponing their travel after their payoff for traveling would have been reduced. Likewise, we would observe people, to whom travel is less valuable, traveling less, if at all, while people, to whom travel is more valuable, would still be traveling.

Increase costs, decrease traffic

To reduce traffic jams, the cost of trips made has to be higher in comparison to the value gained from making the trips, if the amount of traffic is to be reduced. For example, by imposing road tolls such that their costs exceed the value gained from taveling, some people will choose not to travel or postpone their travel to a time, when the collected road tolls are lower or the value of the trip is higher. Here it has to be observed that collecting road tolls on some roads only redirects traffic to roads without tolls. This movement continues, until the value of the time lost in traffic jams on the roads without tolls equals the cost of the road tolls, at which point people are indifferent between using a toll road or one without tolls. To decrease traffic overall, its costs relative to the value gained have to increase on all possible routes.

From the motion’s viewpoint this means that in order to reduce traffic and therefore increase the traffic safety in living areas, heavy traffic would have to be more costly in those areas. Another option would be to ban heavy traffic in those areas, but this would lead to potential congestion and too much traffic on other routes. Just adding capacity by building side routes means that more traffic in total can pass through, but in equilibrium the amount of traffic through the living areas will be such, that it takes as long to reach the destination as it would take by taking the route avoiding the living areas.

 

 

Slow-up

Last weekend I participated to the May 1st Slow-up event. During Slow-up a section of the main streets are closed for motorized traffic for one day, forming a bike route between the participating cities and towns.

The Slow-up I participated in consisted of a 40 kilometer route between multiple towns. Although the weather was rainy, many people participated and spent part of their Sunday riding the route by bike and enjoying the other activities and the food and refreshments organized along the route by local producers, shops and associations.

I only completed part of the route and by foot, so I had some time to think, and I asked myself, what it would take to slow-up on a more permanent basis: How could we make streets less crowded without having negative side effects? Since for example in the EU road transport corresponds to about 73% of the total person kilometer and to about 50% of the total tonne-kilometers, reducing this traffic is no trivial task, since it is the backbone of modern logistics. However, the optimist asks, how to reduce road traffic by replacing it or making part of it redundant, while the pessimist only sees the threats to modern logistics. How to reduce and replace transport of goods and people on the road to make the unavoidable use of the roads more pleasant?

I will be writing a related post to this subject to briefly discuss the incentives and mechanisms in making roads less crowded.

EU Transport in Figures: Statistical Pocketbook 2015
EU Transport in Figures: Statistical Pocketbook 2015

Learning how to teach

At work we have weekly training sessions. Each Thursday one of our team members takes one hour to teach a topic to the rest of the team. The themes range from hands-on use of Excel templates over negotiation skills to creating a business case. The respective theme depends on our annual goals, i.e. what we have agreed to learn, and on the interests of the trainers.

About a week ago I gave our team a training on the Monty Hall problem. The problem is easy to understand, yet the correct answer is somewhat unintuitive and explaining it in an understandable way takes some effort. It also shows well how easy it is to get probabilities wrong. Therefore I had the Monty Hall problem as the day’s topic.

I first presented the problem, and to make it more interesting I asked for volunteers to play against me. This way I wanted to get some statistical data to back up my upcoming explanation of the probabilities in the game. Before starting I presented two questions that we would answer during the training:

  1. Is it profitable to play the game, when the participation costs 0.70 and the potential gain is 1.00?
  2. Which strategy maximizes the expected winnings? And why?

Here I must mention that I introduced the a version of the game, where there is always a prize behind exactly one door, the prize is never removed and the hosts always opens exactly one empty door at random, but never the player’s chosen door.

Before we started playing, one team member asked me for the goal of the training. I replied that the goals were to:

  1. Understand the Monty Hall problem and the related probabilities in general.
  2. To see that probabilities are not always intuitive and thus we should beware when making decision, even if we think we have calculated the risks correctly.

I ended up playing the game with one colleague for ten rounds, so we did not get any statistically meaningful results, but these games already gave us some feeling of the game, how it works and how it feels to be in the situation, having to choose between the doors. After the game I explained the probabilities involved by drawing on a paper the three potential outcomes in a single game and arguing that by changing the initial choice the chances of winning are maximized. This way it was quite easy to convincingly illustrate that sticking to the original door only gives a one in three chance to win.

I think I wan’t able to convince all team members of the importance of understanding the Monty Hall problem or the importance of learning new things outside of your daily business. An in all I was still pleased with how I managed to explain the problem and its essence in a practical and tangible way.

Afterthoughts

The following weekend after the training, when I was again on one of my many walls in the woods, four things dawned to me regarding the lessons given by the Monty Hall problem:

  1. When presenting the Monty Hall problem, it should be thought of as not just as a game of chance, but as a representation of an action containing risk. The game can be thought of as as investment, where the costs and the payoffs determine, whether the investment is profitable.
  2. Even more importantly, the problem teaches us to concentrate on the essential. The game has two stages: In the first stage the player chooses a door and the host opens an empty door. In the second stage the player may change his initial choice. The game can be represented as a one stage game, where the player only makes a decision between choosing one door or choosing two doors. Due to the rules of the game, the host’s opening one empty door is just trickery used to distract the player. If we omit the door opening and give the player the option of choosing either one door or two doors, the intrinsic probabilities of winning become obvious. Thus, it is necessary to see what is relevant.
  3. Based on point 2, when teaching or learning, we should try to present the topic or problem from as many aspects as possible. That way it is easier for more people to learn the subject matter. The multiple representations also enable us to recognize a potentially familiar pattern or situation in a completely different context. This way we can apply the different tools and models we learn. E.g. we might, when presented with an offer, see some similarities to the Monty Hall problem and thus know to be careful in making our choice and are also equipped to analyze the offer correctly.
  4. When teaching, we should emphasize the importance of learning different things and models just to understand how the world might look like. As an analogy, a person with only a hammer is less useful at a construction yard than a person who also has a saw, a grinder, a pen and some paper in his pocket and a crowbar. When we have multiple tools and know how and when to use them, we are better able to act in different situations. With multiple models we are also better equipped to recognize the important things and act accordingly. Sometimes learning something does not provide obvious or immediate benefits, but might later on in life prove to be very valuable.