cs-142 — The Tallied Vote

Problem

Eleven committee members each wrote one name on a slip:

Zoe   Amir  Zoe   Bea   Amir  Cal   Zoe
Bea   Cal   Amir  Zoe

Your deliverables:

1. The tally per candidate.
2. The winner (most slips) and the runner-up.
3. The share of slips for the top two, as percentages of the valid ballots, to one decimal place.
4. The one-sentence announcement to the committee that reports the result without over-claiming (what does 11 slips NOT tell you?).

If the problem is ambiguous anywhere, state the assumption you are making and carry on — a stated assumption is part of a good answer.

Examples

• Input: the eleven slips
• Output: Zoe 4, Amir 3, Bea 2, Cal 2 — winner Zoe 36.4%, runner-up Amir 27.3% — one honest sentence

Solve for the worked instance first. Then ask what would change if one number, name, or condition were replaced by something stranger.

What to notice

• Counting is easy; not over-claiming is the skill. Eleven slips cannot say what the twelfth member or the absentees would have done.
• Percentages must name their base: 4 of 11 valid ballots is not "40%".
• A winner under this rule is defined by the rule (most slips); had the rule required a majority (>50%), the same slips give a different outcome — the rule is part of the result.

Discussion starter

After the solution is revealed, the class spends five minutes on this prompt: "The committee chair asks you to announce 'Zoe wins by a landslide.' Redraft the sentence so it stays true with the same numbers."

Constraints and assumptions

• Difficulty: Beginner (no prior experience assumed).
• Topics: aggregation, communication, data.
• All eleven slips are valid; none is blank or double-named.
• Classroom-scale inputs unless the problem says otherwise.
• Time-box: about five minutes for a first attempt; partial answers with clear reasoning are worth more than silent struggling.
• Optional stretch (not required): describe an alternative approach and say when it beats the obvious one.

Hints and extension

• First nudge: count in one pass, keeping one running number per name.
• If stuck after three minutes, write the input/output line you expect and trace the smallest example by hand.
• After the reveal, attempt the extension below before the next lecture.
• Extension challenge: the chair proposes a two-round runoff between the top two, with Bea's and Cal's slips redistributed by each slip's second choice — explain what information the ballots lack for that, and why.