Florida B.E.S.T. MA.912.LT.3.3
The Standard
Decide voting power within a group using weighted voting techniques. Provide real-world examples of weighted voting and its pros and cons.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students model group decisions with a quota and different vote weights. They calculate each member’s influence, then explain benefits and drawbacks in shareholder, legislative, or council voting.
What Mastery Looks Like
- Given a quota and voter weights, students can list winning coalitions and identify critical voters. They can calculate a Banzhaf power index and use it to judge whether the arrangement is fair.
Common Misconceptions
- Students often assume a voter’s weight equals the voter’s actual power. They may count every member of a winning coalition as critical. They may also miss dummy, dictator, or veto roles, or normalize power values incorrectly.
How to Assess It
- Exit ticket: For [4:3,2,1], list the winning coalitions, mark each critical voter, and report each voter’s normalized Banzhaf power.
Lesson moves
Ways to Teach It
Give teams vote-weight cards and a quota card, then have them build every winning coalition and tag voters whose removal makes it lose.
Ask students to compare shareholder voting with one-person, one-vote, then write one benefit and one drawback of assigning votes by ownership.
Run a coalition race using [7:4,3,2,1], awarding points for each correctly identified critical voter and calculated Banzhaf share.
Use fictional company share totals to design a board vote, then test whether a small shareholder can ever change the outcome.
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Related Standards
- MA.912.FL.1.3
Solve real-world problems involving weighted averages using spreadsheets and other technology.
- MA.912.LT.3
Apply techniques from Election Theory and Fair Division Theory to solve problems.
- MA.912.LT.3.1
Define and explain the basic concepts of Election Theory and voting.
- MA.912.LT.3.2
Analyze election data using election theory techniques. Explain how Arrow’s Impossibility Theorem may be related to the fairness of the outcome of the election.
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