Mathematical Model for Calculating Jury Votes in the Final Stage of a Photo Contest
Including Semifinal and Viewers Ratings
\( F \) — the ranking position a photograph received in the contest. Among all works by an author, the one with the highest score is selected.
\( F = FM + 0.99 \times \left[ \beta SF' + \gamma RE' + \alpha M'_A \right] \)
where:
- \( FM \) — the number of jury votes for a specific work.
- \( SF' \) and \( RE' \) — normalized semifinal and audience ratings (ranging from 0 to 1).
- \( M'_A \) — normalized "author strength" indicator, reflecting the distribution of votes across the author's works (\( \in [0,1] \)).
- \( \alpha, \beta, \gamma \) — weight coefficients. Typically, \( \alpha + \beta + \gamma \leq 1 \) to ensure the total does not exceed 1.
- 0.99 — scaling factor, e.g. to prevent a work with \( FM=4 \) from surpassing a work with \( FM=5 \) in \( F \).
1. Calculation of \( M'_A \) with parameter \( p \)
- For an author \( A \), collect all their works that reached the final.
- Let \( \text{votes}_r \) be the jury votes for work \( r \). Then:
\( M_A = \sum_r (\text{votes}_r)^p \)
- The parameter \( p \geq 1 \) makes high scores "quadratically" (or even more strongly) valuable. For example, at \( p = 2 \), a work with 4 votes gets 16 points, while a work with 1 vote gets 1.
- Normalize \( M_A \) among all authors within \( [0,1] \):
\( M'_A = \frac{M_A - M_{\min}}{M_{\max} - M_{\min}} \)
- Here, \( M_{\min} \) and \( M_{\max} \) are the minimum and maximum \( M \) values across all authors.
2. Meaning of constants \( p, \alpha, \beta, \gamma \)
- \( p \) (exponent in the sum of votes) — allows stronger differentiation (\( p > 1 \)) of high scores.
- \( \alpha \) (weight of "author strength") — determines how important \( M'_A \) is compared to \( SF' \) and \( RE' \).
- \( \beta \) (weight of \( SF' \)) — governs the impact of semifinal ranking after considering \( FM \).
- \( \gamma \) (weight of \( RE' \)) — adjusts the influence of audience ratings.
3. Adjustments
- Increasing \( \alpha \) — gives more weight to authors with many highly-rated works.
- Adjusting \( \beta \) and \( \gamma \) — shifts priority between semifinal ranking and audience rating (the first in our case).
- Modifying \( p \) — fine-tunes how strongly highly-rated works stand out among an author's entries.