Question: Uber, Lyft, and Sidecar are three ride-sharing companies. They enter a competition to see who can pick up the most passengers in three separate locations: Portland, Eugene, and Bend. The winner of the competition is chosen by a judge who evaluates how many passengers each company was able to pick up at each location; the results are summarized in the table below. Since the maximum number of passengers a company can pick up in Bend is typically smaller than the minimum number one can attain in portland, the judge decides to use the following criteria to compare any two companies: if company A beats company B in any two of the three locations, then the judge prefers company A to company B
|
Uber |
Lyft |
Sidecar |
| Portland |
500 |
1200 |
800 |
| Eugene |
150 |
250 |
30 |
| Bend |
70 |
25 |
40 |
Are the judge's preferences transitive? Which company won the competition?