Small classroom market: before interviews
Before interviews
How much the agents agree, how well each side sees the other before interviews, and how concentrated the first choices are.
What to do here
- The tabs above lead to the population, the views before interviews, the applications, the match, and the lists of applicants and programs.
A saved run of the simulator: everyone who opens it sees this same market. Simulated from the assumptions in the parameters; not a prediction of any real applicant's or program's match.
Before interviews
Agreement is the average correlation between two agents' true utilities (1 = everyone agrees). Fidelity is how well the pre-interview view matches the truth: the correlation of true and observed utilities over all pairs, and each agent's rank correlation between its true and its pre-interview ordering.
| Measure | Applicants rating programs | Programs rating applicants |
|---|---|---|
| Agreement (true utilities) | 0.630 | 0.718 |
| Agreement (true rankings, Spearman) | 0.581 | 0.699 |
| Agreement (pre-interview views) | 0.509 | 0.548 |
| Pre-interview noise (SD) | 0.500 | 0.500 |
| Fidelity, expected | 0.894 | 0.894 |
| Fidelity, realised (all pairs) | 0.895 | 0.899 |
| Fidelity per agent (mean Spearman) | 0.862 | 0.884 |
| Distinct first choices | 6 | 4 |
| Share whose first choice is the most popular | 0.667 | 0.375 |
| Share whose first choice is in the top 10 | 1.000 | 1.000 |
| Agents with a taste term | 60 | 8 |
How well does each applicant know their true order?
For each applicant, the rank correlation (Spearman) between their true ordering of every program and their view of it before interviews. 1 is a perfect view; values near 0 mean the pre-interview view says little about the truth. The spread shows how unevenly information falls among applicants. Before interviews only: interviews reveal more, as the Applications and interviews tab shows.
Learn more in the helpApplicants' pre-interview fidelity: 60 applicants in 20 bins from 0.500 to 1.000; the fullest bin holds 12.
The numbers
| From | To | Count |
|---|---|---|
| 0.500 | 0.525 | 1 |
| 0.525 | 0.550 | 1 |
| 0.550 | 0.575 | 0 |
| 0.575 | 0.600 | 0 |
| 0.600 | 0.625 | 1 |
| 0.625 | 0.650 | 0 |
| 0.650 | 0.675 | 1 |
| 0.675 | 0.700 | 0 |
| 0.700 | 0.725 | 0 |
| 0.725 | 0.750 | 0 |
| 0.750 | 0.775 | 5 |
| 0.775 | 0.800 | 5 |
| 0.800 | 0.825 | 2 |
| 0.825 | 0.850 | 3 |
| 0.850 | 0.875 | 6 |
| 0.875 | 0.900 | 6 |
| 0.900 | 0.925 | 12 |
| 0.925 | 0.950 | 5 |
| 0.950 | 0.975 | 8 |
| 0.975 | 1.000 | 4 |
How well does each program know its true order?
For each program, the rank correlation (Spearman) between its true ordering of every applicant and its view of it before interviews. 1 is a perfect view; values near 0 mean the pre-interview view says little about the truth. Before interviews only: interviews reveal more, as the Applications and interviews tab shows.
Learn more in the helpPrograms' pre-interview fidelity: 8 programs in 20 bins from 0.8613 to 0.8999; the fullest bin holds 2.
The numbers
| From | To | Count |
|---|---|---|
| 0.8614 | 0.8633 | 1 |
| 0.8633 | 0.8652 | 0 |
| 0.8652 | 0.8671 | 0 |
| 0.8671 | 0.8691 | 0 |
| 0.8691 | 0.8710 | 1 |
| 0.8710 | 0.8729 | 1 |
| 0.8729 | 0.8748 | 0 |
| 0.8748 | 0.8768 | 0 |
| 0.8768 | 0.8787 | 0 |
| 0.8787 | 0.8806 | 1 |
| 0.8806 | 0.8825 | 0 |
| 0.8825 | 0.8845 | 0 |
| 0.8845 | 0.8864 | 0 |
| 0.8864 | 0.8883 | 0 |
| 0.8883 | 0.8902 | 0 |
| 0.8902 | 0.8922 | 0 |
| 0.8922 | 0.8941 | 0 |
| 0.8941 | 0.8960 | 1 |
| 0.8960 | 0.8979 | 2 |
| 0.8979 | 0.8999 | 1 |
How accurately do applicants see programs?
True against observed utility for a sample of applicant–program pairs: before interviews, the true utility against the pre-interview view; after interviews, for a sample of interviews, the realised utility against the view after the interview. Points on the dashed line are seen exactly; the wider the cloud around it, the noisier the view. The summary gives each cloud's correlation. A sample of at most 1,500 points per series, the same on every visit (drawn from the run's seed).
Learn more in the helpTrue against observed utility, applicants' views of programs: 480 sampled pairs before interviews (correlation 0.895) and 362 sampled interviews after them, realised utility against the post-interview view (correlation 0.98).
How accurately do programs see applicants?
True against observed utility for a sample of program–applicant pairs, before interviews and (for a sample of interviews) after them. Points on the dashed line are seen exactly; the wider the cloud around it, the noisier the view. The summary gives each cloud's correlation. A sample of at most 1,500 points per series, the same on every visit (drawn from the run's seed).
Learn more in the helpTrue against observed utility, programs' views of applicants: 480 sampled pairs before interviews (correlation 0.899) and 362 sampled interviews after them, realised utility against the post-interview view (correlation 0.983).
Is demand concentrated on a few programs?
How many applicants rank each program first before interviews, most wanted first, with each program's number of positions as a mark. Bars far above their mark are programs many more applicants want than they can take. With many programs, zoom with the slider under the chart. First choices before interviews, not the final rank order lists.
Learn more in the helpFirst-choice demand: 6 of 8 programs are some applicant's first choice before interviews; the most wanted tenth of programs gets 66.7% of first choices (Gini 0.704).
The numbers
| Program | Rank it first | Positions |
|---|---|---|
| Program 6 | 40 | 2 |
| Program 8 | 11 | 3 |
| Program 5 | 3 | 4 |
| Program 2 | 2 | 4 |
| Program 4 | 2 | 8 |
| Program 7 | 2 | 8 |
| Program 1 | 0 | 8 |
| Program 3 | 0 | 13 |
How unequal is first-choice demand?
The Lorenz curve of first-choice demand: programs from the least to the most wanted, against their cumulative share of first choices. The dashed diagonal is equal demand; the further the curve sags below it, the more concentrated demand is. The Gini coefficient in the summary is twice the area between them (0 = equal, 1 = everyone wants the same program).
Learn more in the helpThe Lorenz curve of first-choice demand: programs from the least to the most wanted against their cumulative share of first choices; the dashed diagonal is equal demand, and the Gini coefficient (0.704) is twice the area between them.