The *WTA* (Winner-Take-All) award system lurks in every aspect of human affairs, and it is particularly evident in competitive games and markets. There are several aspects of WTA mechanism that are not fully appreciated. In this section, we will examine the WTA mechanism in the simplest context – in a competitive games in which only a limited number of participants receive any type of awards.

It is instructive to start with some visual display of competitive outcome in which the WTA mechanism is clearly in operation. In order to make the underlying mechanism visible and the hidden parameters explicit, we will rely on a simple computer simulation of Olympic-like competition. In the Summer Olympics, there are 302 or so medal events, and in each event three medals are awarded. In the following simulation, we duplicate the conditions of the Olympic (medal) events: 302 events, total 187 competitive teams (or nations), and three medals with different points awarded (3 for Gold, 2 for Silver, and 1 for Bronze). (When we simulate situations in which more medals are given for an event, the award-points are determined by reversed-ranking order.) The simulation assumes that the actual performance depends on two components (T: the underlying capacity and E: the random error) and their relative weight in determining the actual performance or outcome.

### Computer Simulation of WTA (Winner-Take-All) Award Systems

```
```

```
```

` `

First, examine the graph, with default parameter specifications: the simulation assumes that three medals are awarded in each event (N-Winners = 3), the proportion of error variance is assumed to be 50% (errorvar = .5), and it shows the results of one Olympic-like Game (N-Trials = 1). Actual performance in each event is assumed to be the combined product of the true underling strength and the random error component. In this case, it is assumed that error and true components have equal weights. Note that the relationship between the underlying capacity and the award-outcomes is severely non-linear and there is a clear and systematic bias that favors the most powerful: award points are highly concentrated at the top of the power scale.

Now play the interactive graph, by choosing different parameters in turn on each of the three parameters. When you do, you will find out that:

- the greater the WTA tendencies (as the number of winners gets smaller) the greater the non-linearity (and the greater the degree of concentration)
- the smaller the role of random errors, the greater the nonlinearity and the greater the concentration
- the greater the number of trials aggregated, the less the scatter or noises around the given non-linearity pattern, but it does not affect the degree of non-linearity
- the combined (joint) effects are not additive: the effects of the WTA parameter and the error component parameters are interactive

*Most people, including many policy makers and scholars are likely to mistake the medal-points hierarchy as a rough reflection of power-hierarchy, because almost all available quantitative indices of national power show similar pattern. There are two important messages to note:*

- because of the ubiquity of WTA effects, the outcome based measures
*cannot*be used as credible indicators of the underlying capacity; - the prevailing misperceptions are likely to impute unwarranted social status, honor, or power to those few at the top of the power-hierarchy.

### Proportionate Award System

The simplest way to appreciate the ubiquitous nature of winner take all system is to consider how rarely, if ever, we use a “proportionate” award system, in which all the participants receive awards that are proportional to their actual performance or achievement. In theory, we can think of such a system, but the implementation of such award system is impractical or down-right impossible. Nevertheless, it is important to know their theoretical implications.

In the following we present a computer simulation in which an Olympic Game like situation is created and see what happens if we were to provide some kind of award to all participants, awards being varied, proportional to the relative performance level of each participant. Imagine a hypothetic 100m dash in which n-number of people run, and the awards are handed out inversely proportional to their differences in times to finish.

```
```

```
```

` `

Please play around the interactive graph. The parameters may affect the degree of scatters around a linear trend, but not much else. The important point is that, at least, in theory, we can produce a competitive system in which the outcomes can be aggregated to correctly reflect the underlying capacity. But, in real life, such situation is rarely realized.

Another way to produce a proportional award system is to create a round-robin tournaments, in which every team or participant plays every other participant, and aggregate the points acquired by each team. But such a tournament system is impractical if the number of participants is greater than 8, and we only see them in practice with four teams at most(for instance, World Cup uses this formula at some stages of competition).