Lecture: Political Participation: Parties, Elections & Voting Systems
Lecture script · about 15–20 minutes spoken · Week 11
Opening
Picture a student club with 30 members choosing a president. Three people run, and the votes come in 12, 10, and 8. The person with 12 wins, and everyone goes home. But 18 members voted for somebody else. Under a different counting rule, the club would vote again.
That's the whole week in one small room. You meet counting rules everywhere. Maybe you're a business major watching shareholders fill a company board. Maybe you're a nursing student electing a staff council at a hospital. Maybe you're choosing club officers. In every case the rule decides who wins before anyone casts a ballot. In this lecture you'll learn to see how.
Here's where we are. Week 1 gave you the line between empirical and normative claims. Week 5 showed that free, fair, competitive elections are the floor of democracy. Week 7 built parliamentary governments and treated coalitions as normal. Week 8 gave you the three-layer read: design, practice, and verdict. Week 10 studied the U.S. case. Now we ask how citizens take part, and how their votes become seats.
I'll start with plurality and majority, then meet the parties. We'll sort four families of electoral rules and name them in four made-up countries. Then we'll work a seat table, meet Duverger's law, and read a real election. We'll close on traps and on a debate I won't settle for you. Next comes Week 12, on public opinion and polls.
1. Plurality versus majority
Back to the club. Every number in it is illustrative, invented for teaching. The winner had 12 of 30 votes. Divide 12 by 30 and multiply by 100, and you get 40 percent.
Here are the two words. A plurality is the largest number of votes among the candidates or parties, whether or not it is more than half of all the votes cast. A majority is more than half of the votes cast or of the seats available. Half of 30 is 15, so a majority of the club needs 16.
So the winner had a plurality and not a majority. Under a "most votes wins" rule, that's enough. Under a rule that demands a majority, the top two, with 12 and 10, would meet again.
Here's the mistake to watch for. People use the two words as if they meant the same thing. They don't. A plurality is the biggest pile. A majority is more than half.
Pause and try this. In the club, the second candidate had 10 votes. Was that a plurality, a majority, or neither?
Compare 10 with the other piles first.
Here's the answer. It's neither, because 12 is a bigger pile, and 10 is well short of the 16 a majority needs.
2. The parties and the party system
Think about a group project with eight people. Somebody pulls the ideas into a plan. Somebody gets everyone to show up. And when it goes badly, the whole group can see whose plan it was. Parties do those jobs for a whole country.
A political party is an organized group that competes under a common label to win public office and so shape government and policy. Parties do three jobs. Aggregation gathers many separate interests into one program. Mobilization gets people to register, vote, and take part. Accountability gives voters a known label to reward or punish at the next election.
Step back and look at a whole country, and you can describe its party system, the usual pattern of competition among its parties. In a two-party system, two big parties win nearly all the seats. In a multiparty system, three or more parties win real shares. In a dominant-party system, several parties compete but one keeps winning. Each one describes a steady pattern. None of them is a verdict.
Pause and try this. Volunteers drive older neighbors to the polls on election day. Which of the three party jobs is that?
Run through the three jobs before you choose.
Here's the answer. It's mobilization, because the volunteers are helping people take part rather than building a program or answering for a record.
3. Four families of electoral rules
An electoral system is the set of rules that turns the votes cast in an election into seats or offices won. We sort the world's systems into four families. That's a classroom model, a simplification; real systems blend them.
The first family is plurality, or first-past-the-post. Each single-member district elects one member, and the most votes wins, majority or not. Proponents say it's simple, ties each member to a place, and tends to produce single-party governments voters can hold to account. Critics say many votes elect no one, and thinly spread parties get shut out.
The second family is majority-runoff. If no one wins more than 50 percent, the top two meet in a second round. Proponents say the winner ends with majority support. Critics say voters must come back twice, and smaller parties still get squeezed.
The third is proportional representation. Seats go to parties in line with their vote shares, usually from party lists, and usually with an electoral threshold, a minimum share before a party wins any seats. Proponents say seats track votes. Critics say the local tie weakens and coalitions become normal.
The fourth is mixed-member proportional. You get a district vote and a list vote, and list seats top up each party toward its list share. Proponents say it keeps local members and tracks votes. Critics say it's complex.
Pause and try this. Which family asks a second question only when the first round has no winner above 50 percent?
Picture the club voting a second time.
Here's the answer. It's majority-runoff, because a second round happens only when nobody clears half of the votes.
4. Naming the family in four made-up countries
There's one fast question that names a family: how is a winner decided? Let's try it on four invented countries. Every number in them is illustrative.
In Tavrenia, each of 100 districts elects whoever has the most votes, and one district's winner has 38 percent. That's first-past-the-post. In Halvenor, the president needs more than 50 percent, and the first round splits 41, 35, and 24. Nobody clears 50, so the top two meet again. That's majority-runoff.
In Lunmara, 120 seats are shared out from party lists by vote share, with a 5 percent threshold. That's proportional representation. In Vessaly, voters cast a district vote and a list vote for 120 seats, 60 of each kind. Party X wins 40 districts and 35 percent of the list vote. Take 35 percent of 120 and you get 42, so Party X gets 2 list seats to reach its proportional total. That's mixed-member proportional.
Pause and try this. In Lunmara, a small party wins 4 percent of the vote. Does it win any seats?
Hold the threshold in your head.
Here's the answer. It wins no seats, because 4 percent is below Lunmara's 5 percent threshold.
5. The D'Hondt table
Imagine four friends splitting eight slices of pizza by how much each paid. Nobody gets half a slice. Proportional systems face the same problem, because seats come whole. One common fix is the D'Hondt method: divide each party's votes by 1, 2, 3, and so on, pool every result, and give the seats to the largest results until they run out. Each result is a quotient.
Here's the illustrative table. Four parties share 100,000 votes in one district with eight seats. Party A has 48,000, Party B has 30,000, Party C has 14,000, and Party D has 8,000. Divide A by 2 and you get 24,000. By 3, 16,000. By 4, 12,000. By 5, 9,600. Party B gives 15,000, 10,000, and 7,500. Party C's second quotient is 7,000, and Party D's is 4,000.
Now rank the pool. The eight biggest are 48,000 for A, 30,000 for B, 24,000 for A, 16,000 for A, 15,000 for B, 14,000 for C, 12,000 for A, and 10,000 for B. So A wins 4, B wins 3, C wins 1, and D wins none. The trap is ranking one party at a time. Generate every party's quotients first, then rank the whole pool.
Pause and try this. Party A's fifth quotient is 9,600. Why doesn't it win a seat?
Count where 9,600 lands in the ranking.
Here's the answer. It's the ninth-largest quotient, and the eight seats are gone before the ranking reaches it.
Now the contrast. Put the same votes in eight single-member districts, with A leading in every one. Under first-past-the-post, A wins 8 of 8. Same votes, different rule, different chamber.
6. Duverger's law
Suppose you like the candidate running a distant third. Plenty of people in your spot vote for a second choice instead, so their vote isn't wasted. Add that up across a country and you get a famous idea.
Duverger's law comes from Duverger in 1951, in a book called Political Parties, translated into English in 1954. I'll teach it in words. It's the tendency of single-member plurality rules to produce competition between two main parties. It works two ways. The mechanical effect is the counting rule itself: a third party with scattered votes wins few seats. The psychological effect happens before the vote: voters desert parties they expect to lose.
The key word is tendency. A tendency has a mechanism and holds in most cases, but real cases can break it. Duverger's law has named exceptions. The United Kingdom, Canada, and India all use plurality rules, and all still seat significant third or regional parties.
Pause and try this. Supporters of a trailing party switch to a bigger party before election day. Which effect is that?
Ask whether it happens at the count or before it.
Here's the answer. It's the psychological effect, because expectations changed the votes before any counting happened.
7. Reading the 2024 UK result
Now real data, from the House of Commons Library's briefing on the 2024 UK general election. The election used 650 single-member constituencies under plurality rules, and turnout was 59.7 percent. Read it with five questions: what's measured, over whom and when, what it shows, what it doesn't, and whether it's correlation or cause.
Labour won 33.7 percent of the vote and 411 seats. That's 411 divided by 650, about 63.2 percent of the seats. The gap is 29.5 percentage points. Percentage points are the unit for the difference between two percentages. Reform UK won 14.3 percent of the vote and 5 seats, about 0.8 percent of the chamber. The Liberal Democrats won fewer votes, 12.2 percent, and 72 seats. The Scottish National Party won 2.5 percent and 9 seats.
What does it show? A vote that's geographically efficient converts into seats, and a dispersed one doesn't. What doesn't it show? Whether that's fair, or whether the rules should change. Is the gap a cause or a correlation? The claim that plurality rules produced it rests on an explicit argument, the mechanical effect. The table alone can't show how people would have voted under another rule.
Pause and try this. Labour's 63.2 and 33.7 are both percentages. Which one is the vote share?
Ask what each percentage is a share of.
Here's the answer. It's 33.7, because that's Labour's share of the votes cast, while 63.2 is its share of the 650 seats.
8. Three traps
Three wrong turns catch almost everyone once. First: "the party with the most votes always wins the most seats." Under plurality rules, seats depend on where votes land. Reform UK had more votes than the Liberal Democrats and far fewer seats.
Second: "proportional representation produces stable single-party government." The opposite is more typical. When seats track votes, one party wins half the seats alone only if it wins about half the votes, so coalitions are the more typical result, the normal mode you met in Week 7.
Third: "a seat majority proves a mandate." A mandate is the claim that an election result gives the winner the voters' authority to carry out its program. That's a normative judgment, and a seat count doesn't settle it by itself. Labour's 411 seats are a fact on the practice layer. Whether 411 seats on 33.7 percent of the vote are a mandate is an argument on the verdict layer.
Pause and try this. A commentator says, "They won 411 seats, so voters ordered every promise." Which part is empirical?
Split the sentence at the word "so".
Here's the answer. The 411 seats are the empirical part, checkable against the official count, and everything after "so" is a normative claim the count can't settle.
9. First-past-the-post or proportional representation?
Here the facts stop and the argument starts. Proponents of first-past-the-post argue for clear accountability, because one party usually governs alone. They value a local member for every place. And they like governments that can act without bargaining with partners. Remember the plurality contrast: 8 of 8 seats for a party with a lead.
Proponents of proportional representation argue that seats should match votes. They say no large group of voters should elect no one. And they argue that coalitions make each decision represent more of the country.
Each side names a real cost in the other. First-past-the-post can hand a big seat majority to a party most voters didn't choose. Proportional representation can let a small party make or break a coalition, and it loosens the local tie. Which cost is worth paying depends on what you value. That's normative, and the verdict is yours.
Pause and try this. "Seats should match votes." Is that an empirical claim or a normative one?
Notice the word "should" in it.
Here's the answer. It's normative, because it says what ought to happen and can only be argued from values, not checked against a count.
Closing
Let me pull it together. A plurality is the most votes, and a majority is more than half. Parties aggregate, mobilize, and answer for their record, and a party system describes a pattern, not a verdict. The four families are first-past-the-post, majority-runoff, proportional representation, and mixed-member proportional, and you name them by asking how a winner is decided. D'Hondt means every quotient first, then rank the pool: 4, 3, 1, and none. Duverger's law is a tendency with two effects and named exceptions. In 2024, 33.7 percent of the vote became 411 of 650 seats, and 14.3 percent became 5. Seats are counted, and mandates are argued. First-past-the-post or proportional representation is your call.
Next in this module come the slide deck, the Readings and Resources page, the lecture tutorial, the practice set, the quiz, the discussion, and the assignment. Then Week 12, Public Opinion, Political Behavior & the Media, asks how a small, careful poll can speak for a whole country.
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