Weighted Voting of Three Models

Weighted Voting of Three Models

English translation by SOTA – AI Community of the Russian original. Organisers who would like this translation removed can email [email protected].

Task 8 of the school stage (Moscow) of the All-Russian School Olympiad (VsOSh) 2025/26 in artificial intelligence, grades 9–11. Original: tasks-ai-9-11-sch-msk-25-26.pdf.

Using three machine learning models $a_1, a_2, a_3$, we want to distinguish photographs of dogs (class 0) from photographs of cats (class 1). To evaluate the quality of the models, we ran them on a set of images for which the correct answer is known.

In the table (XLSX format, CSV format), each row contains four numbers: column $y$ gives the correct class, and columns $a_1, a_2, a_3$ give the answers of the three models. All the numbers are equal to 0 or 1.

Translator's note: the PDF contains no links to the data files named here.

The models are trusted to different degrees; the weights are set as follows:

$$w_1 = 2, \qquad w_2 = 1, \qquad w_3 = 3.$$

For each row, the weighted sum is computed:

$$S = w_1 \cdot a_1 + w_2 \cdot a_2 + w_3 \cdot a_3.$$

The final answer is $\hat{y} = 1$ if $S \geq 3$, and $\hat{y} = 0$ otherwise.

Find the number of rows in which the final answer $\hat{y}$ matches the correct answer $y$. Give only this number as your answer.

Translator's note: the statement paper gives only the total for the olympiad (112 points); the official solutions give this task a maximum of 12 points (exact match of the answer).