Electoral Systems and Political Parties History Education helps students see politics not only as events and personalities, but as designs that shape behavior. By working with histories of electoral rules and real election outcomes, learners practice asking disciplined questions: What counts as fair representation? How do different voting systems reward coalitions, polarize societies, or encourage moderation? These guiding standards and comparisons keep the study from becoming mere storytelling, turning it into careful analysis of how institutions channel power. Supported by scholarly expertise, reliable records, and well-chosen case studies, students build lasting outcomes: they learn the main families of electoral systems, understand how party systems emerge and evolve, and gain the skill to interpret election results in context—linking numbers and narratives to the deeper structure beneath them.
The evolution of electoral systems and political parties reveals the complexity of governance, representation, and legitimacy in societies throughout history. As forms of democracy developed, so too did the structures that underpin them—voting mechanisms, party institutions, and ideological movements that shape the political landscape. The broader study of history provides essential context for understanding how these systems emerged, adapted, and influenced national destinies.
At the heart of this narrative is the deep connection between ideas and institutions. Early influences from intellectual political history and political ideologies shaped the frameworks within which elections were contested and governments were formed. These ideologies were often fueled by economic contexts, as explored in economic thought and theory, and by broader shifts in industrial and technological history.
Electoral reform movements often coincided with demands for equality and justice. The development of suffrage and civil rights movements challenged exclusionary systems, while questions around electoral fraud and integrity underscored the need for transparent governance. These challenges were shaped by larger social forces, including social movements and changes in social history.
As political parties institutionalized around distinct platforms, they became channels for negotiating interests tied to labor history and labor and social policy. Political developments in different regions reflected varying historical conditions—ranging from alliances explored in history of alliances to local transformations in urban and rural history.
Technology also played a critical role in reshaping electoral environments. The role of technology in elections introduced new dynamics, including digital campaigning and voter data analytics, while war and conflict—as studied in social and cultural history of warfare and technological history of warfare—often disrupted or reshaped electoral systems in contested regions.
The global nature of party politics is also evident in economic and trade policies. Electoral agendas frequently reflect positions on international agreements, as seen in treaty analysis and debates in trade and commerce history. As globalization accelerated, national parties increasingly responded to pressures from global capital and foreign policy demands.
Education served as both a battleground and a tool for political socialization, examined in education history, while political legitimacy often depended on historical narratives—ranging from the shaping of electoral history to mobilization strategies resembling those in guerrilla warfare and insurgency studies.
Finally, understanding the evolution of parties also means recognizing who has been excluded. Insights from women’s history and other marginalized narratives add crucial depth to the story of political systems—emphasizing not just the function of parties, but who they serve, and how representation has been won, denied, or reshaped across generations.
Organising Power: Elections, Parties, and Political Competition
Modern political systems rely on structured competition. Electoral systems determine how votes are translated into representation, while political parties organize ideas, mobilize support, and compete for power. Together, they shape how citizens participate and how governments are formed.
History of Political Systems – Overview
Trace how different forms of governance evolved and how political authority is structured across societies.
Political Ideologies
Explore how competing doctrines and belief systems are organized and expressed through political party platforms.
Military & Political Power
Examine how electoral political competition interacts with armed force and state structures of control.
Electoral Systems & Political Parties (Current Module)
Study how voting mechanics, district rules, and party structures determine representation, competition, and government formation.
Constitutional History
Understand how legal charters and constitutional frameworks define franchise rights, election rules, and party regulation.
Comparative Politics
Compare how different political systems organize cross-national party competition, election rules, and democratic representation.
Colonial & Post-Colonial Systems
Investigate how electoral institutions and party systems evolved under colonial rule and post-independence state-building.
Bureaucratic & Administrative History
Examine how permanent civil service structures and independent electoral commissions support election management.
Essential Features in Electoral Systems
Definition and Purpose
Electoral systems refer to the legal and institutional rules that govern how votes are cast, tallied, and converted into legislative seats or executive offices.
Core Functions
- Representation: Ensures the preferences, demographics, and political voices of the electorate are mirrored in governing bodies.
- Accountability: Establishes institutional mechanisms for citizens to retain or dismiss political leaders through periodic elections.
- Government Stability: Facilitates the formation of stable executive cabinets and promotes legislative continuity.
Types of Electoral Systems
Electoral systems are categorized based on their voting formulas, district magnitudes, and seat conversion mechanisms.
Majoritarian Systems
Priority is placed on manufactured majorities to ensure strong, single-party executive governance.
- First-Past-The-Post (FPTP): Single-member districts where the candidate securing a plurality of votes wins (e.g., United States, Canada, India).
- Two-Round Majority System: If no candidate secures an absolute majority (50% + 1) in the first round, a runoff is held between top contenders (e.g., French presidential elections).
Proportional Representation (PR)
Priority is placed on mirroring voter preference proportions in the legislature.
- Party-List System: Voters cast ballots for party slates, with seats allocated based on national or regional vote share percentages (e.g., South Africa, Israel).
- Single Transferable Vote (STV): Multi-member districts where voters rank candidates numerically, transferring excess votes via a quota formula (e.g., Ireland, Malta).
Mixed Systems
Combines majoritarian district representation with proportional party-list balance.
- Mixed-Member Proportional (MMP): Voters cast two ballots: one for a local district representative and one for a party list, using list seats to compensate for majoritarian disproportionality (e.g., Germany, New Zealand).
Electoral Processes and Reforms
Expansion of Universal Suffrage
- Historical expansion of voting rights from elite property-owning men to universal adult suffrage regardless of class, race, or gender (e.g., the U.S. 19th Amendment in 1920, South Africa’s democratic transition in 1994).
Election Administration & Technology
- Impartial election management bodies (EMBs) safeguard voting integrity against fraud, while electronic voting and digital auditing modernize ballot counting.
Core Roles and Responsibilities of Political Parties
Definition
Political parties are organized associations that seek to exercise governmental power by nominating candidates, contesting elections, and formulating public policy.
Core Functions
- Interest Aggregation & Representation: Channeling diverse societal demands into coherent policy platforms.
- Mobilization & Socialization: Engaging voters, organizing campaigns, and fostering civic participation.
- Leadership Recruitment: Training, selecting, and supporting candidates for public office.
- Government Formation & Opposition: Organizing legislative majorities or providing structured scrutiny as opposition.
Types of Party Systems
Single-Party Systems
A single political party holds a legal monopoly on power, restricting political opposition (e.g., China under the CCP).
Two-Party Systems
Two dominant parties consistently win the overwhelming majority of legislative seats and executive elections, often fostered by FPTP rules under Duverger’s Law (e.g., the United States).
Multi-Party Systems
Multiple parties win seats in legislature, requiring coalition government formation (e.g., Germany, India, Netherlands).
Practical Real-World Implementations
- British Parliamentary System: FPTP voting drives two-party dominance between Labour and Conservatives.
- U.S. Federal System: FPTP combined with the Electoral College reinforces a strict two-party framework.
- German MMP System: Dual-vote ballots balance local constituency accountability with proportional party representation.
Challenges and Critiques
- Majoritarian Disproportionality: Majoritarian rules can produce “wasted votes” and penalize third parties.
- PR Instability: Extreme proportional systems can lead to legislative fragmentation and unstable coalition collapse.
- Polarization & Patronage: Hyper-partisanship and patronage networks can erode public trust in electoral institutions.
Why Delve into Studying Electoral Systems and Political Parties
Understanding the Mechanics of Representation and Democracy
Exploring the Variety and Impact of Electoral Systems
Analyzing the Role of Political Parties in Organizing Politics
Recognizing the Challenges of Electoral Integrity and Party Reform
Preparing for Study in Political Science, Law, and Public Affairs
Electoral Systems and Political Parties: Final Reflections
The study of electoral systems and political parties highlights their critical role in shaping governance, representation, and political participation. From the introduction of universal suffrage to the rise of multi-party systems, these institutions have evolved to meet the challenges of diverse and dynamic societies. By examining their structures and processes, we gain a deeper understanding of the mechanisms that sustain democracy, address societal needs, and influence the global political landscape.
Interactive Model: D’Hondt Proportional Representation Seat Allocation Simulator
Adjust national vote percentages for 4 political parties and total district magnitude to observe real-time proportional seat allocation via the D’Hondt highest-averages method over a 5-election timeline.
Interactive Review Questions
How does First-Past-The-Post (FPTP) differ from Proportional Representation (PR) in converting votes to seats?
What is Duverger’s Law and how does it explain party system formation?
What is a Mixed-Member Proportional (MMP) electoral system?
Why are multi-party systems more prone to coalition government formation?
Frequently Asked Questions
What is an electoral system?
An electoral system is the set of rules that translates votes cast in an election into seats in a legislature or other representative body. It includes how districts are drawn, how many representatives are chosen, how ballots are structured, and how votes are counted to determine winners.
How do electoral systems relate to political systems more broadly?
Electoral systems are one of the key mechanisms through which citizens connect to the state. They shape how power is contested, who can realistically win office, and how governments are formed. Over time, changes in electoral systems have often accompanied broader constitutional reforms, democratisation, and shifts in party politics.
What are the main types of electoral systems?
The main families of electoral systems are plurality/majoritarian systems (such as first-past-the-post or two-round systems), proportional representation systems (such as party lists or single transferable vote), and mixed systems that combine elements of both. Each type produces different patterns of representation and party competition.
How do electoral systems influence the number and type of political parties?
Electoral systems strongly affect party systems. Plurality/majoritarian rules in single-member districts tend to favour larger parties and encourage two-party competition, while proportional representation makes it easier for smaller parties to win seats and often supports multi-party systems. Over time, these incentives shape how parties form, merge, and campaign.
What is meant by a political party in historical perspective?
A political party is an organised group that seeks to influence or control government by winning elections and placing its members in public office. Historically, parties evolved from loose factions around powerful individuals into structured organisations with memberships, programmes, and national networks that connect voters to institutions.
How have political parties developed over time?
Party development has moved from elite factions in parliaments to mass parties linked to social classes, churches, trade unions, or nationalist movements, and later to catch-all or professionalised parties focused on broad electoral appeal. Electoral rules, social change, and media technologies have all shaped how parties recruit members, choose leaders, and communicate with voters.
What is the relationship between electoral reform and party politics?
Electoral reform—changing district boundaries, voting rules, or seat formulas—can alter the strategic environment for parties. Parties may support or resist reforms depending on whether they expect to gain or lose seats, and reforms can trigger shifts in alliances, the emergence of new parties, or changes in how parties campaign and govern.
How do electoral systems affect representation of minorities and women?
Electoral systems can make it easier or harder for minorities and women to gain office. Proportional representation and multi-member districts often provide more opportunities for diverse candidate lists, while some systems use reserved seats or gender quotas. Historical research shows that institutional design interacts with social norms and party strategies to shape who is elected.
What is a party system, and how is it studied historically?
A party system refers to the overall pattern of competition among parties in a country: how many parties matter, how stable they are, and how they relate to voters and to each other. Historians and political scientists identify dominant-party, two-party, and multi-party systems, and examine how they evolve in response to social cleavages, institutional changes, and major events.
What is meant by realignment or reconfiguration of party systems?
Realignment occurs when the main lines of party competition shift—for example, when new issues such as religion, class, nationalism, or the environment reshape voter loyalties and party identities. Over time, this can transform which parties are strong, who their core supporters are, and how electoral coalitions are built.
How have technological and media changes influenced elections and parties?
From the spread of newspapers and radio to television, social media, and data-driven campaigning, communication technologies have changed how parties reach voters, frame issues, and organise campaigns. Electoral history tracks how these innovations altered campaign styles, party organisation, and the visibility of candidates and issues.
Why is it important for students to study electoral systems and political parties historically?
Studying electoral systems and parties historically shows that the rules of voting and the structure of party competition are not fixed: they are designed, debated, and revised. This perspective helps students understand why some voices are louder than others in politics, how institutional choices shape democracy and representation, and how reforms might address contemporary challenges such as polarisation, disengagement, or unequal representation.
Comprehensive Mastery & Practice Module
Section 1: Foundational Core Knowledge Verification
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What are electoral systems and how do they shape political representation?
Answer: Electoral systems are the methods and rules by which votes are translated into political power, directly affecting how representatives are elected and how political preferences are expressed. They determine the structure of political representation by influencing the allocation of seats in legislative bodies. Different electoral systems can lead to varying degrees of proportionality, affecting the fairness and inclusiveness of political outcomes. As a result, electoral systems play a crucial role in shaping the overall dynamics of governance and political accountability. -
How do major types of electoral systems differ in allocating seats?
Answer: Major electoral systems, such as majoritarian, proportional, and mixed systems, differ fundamentally in how they convert votes into seats. In majoritarian systems, the candidate with the most votes typically wins, which can lead to a concentration of power and a two-party system. Proportional representation systems allocate seats in line with the percentage of votes each party receives, promoting multi-party competition and diverse representation. Mixed systems attempt to combine these approaches to balance local representation with proportional fairness, resulting in complex electoral outcomes. -
What role do political parties play in electoral systems?
Answer: Political parties are central to electoral systems, serving as the primary vehicles for organizing political competition and aggregating voter interests. They help structure electoral contests by presenting coherent policy platforms and mobilizing voter support. Parties also influence the design of electoral systems, as different systems may favor the development of either large, dominant parties or a broader array of smaller parties. Through their participation, political parties contribute to the functioning of democratic processes and the stability of governance. -
How have historical developments influenced modern electoral systems?
Answer: Historical developments have played a significant role in shaping modern electoral systems, as past experiences with governance, social movements, and political reforms have driven changes in electoral design. Early experiments with voting procedures and representative assemblies laid the foundation for contemporary electoral practices. Over time, reforms have been implemented to address issues such as fairness, inclusivity, and the effective translation of votes into representation. These historical shifts continue to inform current debates and innovations in electoral system design. -
What are the advantages and disadvantages of proportional representation?
Answer: Proportional representation offers the advantage of reflecting the diverse spectrum of voter preferences by allocating seats in accordance with the percentage of votes received, thus ensuring a more inclusive representation. This system tends to encourage multi-party participation and can lead to more consensus-based policymaking. However, it may also result in fragmented legislatures with numerous small parties, which can complicate the formation of stable governments. Additionally, proportional systems sometimes lead to coalition governments that may struggle with internal disagreements and policy coherence. -
How does a majoritarian electoral system impact political competition?
Answer: A majoritarian electoral system tends to concentrate power by awarding victory to the candidate or party with the most votes, often leading to a two-party system. This can simplify voter choices and lead to clear majorities in legislative bodies, promoting decisive governance. However, such systems may marginalize smaller parties and minority interests, reducing the diversity of political representation. The competitive dynamics in majoritarian systems can also incentivize strategic voting and may result in polarization between the dominant parties. -
In what ways do mixed electoral systems combine elements of different methods?
Answer: Mixed electoral systems combine elements of both majoritarian and proportional representation systems to balance local representation with overall proportionality. They typically allocate some seats based on single-member districts while filling additional seats through party lists to ensure that the overall distribution of seats mirrors the national vote share. This hybrid approach can help reconcile the advantages of local accountability with the benefits of a proportional outcome. However, the complexity of mixed systems may lead to challenges in voter understanding and potential inconsistencies in electoral outcomes. -
How have electoral reforms evolved in response to changing political landscapes?
Answer: Electoral reforms have evolved over time as societies have sought to improve the fairness, transparency, and inclusiveness of their voting systems. Changes such as the introduction of secret ballots, the expansion of the franchise, and adjustments to voting methods have been implemented to address historical inequities and adapt to new political realities. These reforms often reflect shifts in public values and technological advancements, aiming to enhance democratic participation and representation. The continuous evolution of electoral systems highlights the dynamic relationship between political institutions and the societies they serve.
Section 2: Advanced Analytical & Scenario-Based Inquiry
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How might emerging digital technologies transform traditional electoral systems and political party dynamics?
Answer: Emerging digital technologies transform electoral systems by streamlining vote counting, enhancing voter registration, and enabling real-time analytics. These advancements improve transparency and efficiency, but also introduce cybersecurity risks and digital manipulation concerns. Digital platforms allow political parties to bypass traditional media hierarchies and engage directly with voters, shifting power toward agile, issue-based movements while altering campaign strategy. -
What are the potential consequences of electoral system reforms on democratic stability and representation?
Answer: Reforming an electoral system alters the translation of votes to power. Transitioning from FPTP to Proportional Representation enhances minority representation and pluralism, but may lead to legislative fragmentation and difficult coalition building. Conversely, adopting majoritarian rules promotes executive stability at the cost of penalizing third parties and underrepresenting minority preferences. -
How can comparative analysis of electoral systems inform the design of more inclusive political institutions?
Answer: Comparative analysis highlights how institutional design choices—such as district magnitude, list structures, and gender quotas—directly impact the election of women and marginalized minorities. Examining cross-national best practices allows constitutional designers to tailor hybrid electoral frameworks that reconcile local constituency representation with proportional fairness. -
In what ways do cultural factors influence the formation and success of political parties within different electoral frameworks?
Answer: Cultural values shape voter expectations regarding collective welfare versus individual liberty. In societies with strong communal or regional identities, political parties align along ethno-linguistic or religious cleavages. Electoral rules interact with these cultural cleavages: PR encourages distinct cultural parties, whereas FPTP forces multi-ethnic coalitions within broad "catch-all" parties. -
How do electoral systems shape the strategic behavior of political parties during campaigns and elections?
Answer: Majoritarian FPTP systems incentivize parties to target swing constituencies and adopt moderate, broad-appeal messaging to secure district pluralities. Proportional systems encourage parties to mobilize specific core demographics and establish distinct ideological platforms, anticipating post-election coalitional bargaining. -
What lessons can be learned from historical electoral reforms to address contemporary challenges in voter engagement?
Answer: Historical reforms demonstrate that expanding electoral access—such as secret balloting, lowering voting ages, and removing property restrictions—increases civic trust and participation. Combining administrative accessibility with non-partisan voter education boosts turnout and counteracts disenfranchisement. -
How does the interplay between media, technology, and electoral systems affect political polarization?
Answer: Algorithm-driven media echo chambers exacerbate partisan polarization by incentivizing outrage. When combined with majoritarian FPTP systems, parties are encouraged to deploy outrage-based mobilization in primary elections, hardening partisan divides and undermining legislative compromise. -
What role do political party ideologies play in shaping the evolution of electoral systems over time?
Answer: Party self-interest and ideology drive electoral engineering. Left-leaning and minority parties historically advocated for Proportional Representation to overcome majoritarian entry barriers, whereas dominant ruling parties defend majoritarian FPTP rules to preserve single-party legislative majorities.
Section 3: Quantitative Electoral Mechanics & Formula Problems
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D'Hondt Seat Allocation Formula: In a 4-seat multi-member district, Party A receives 42,000 votes, Party B receives 27,000 votes, and Party C receives 15,000 votes. Allocate the 4 seats step-by-step using the D'Hondt quotient formula V / (s + 1), where V is total party votes and s is current seats won.
Solution:
Initial quotients (seats won = 0): A = 42,000 | B = 27,000 | C = 15,000.
Step 1: Highest quotient is 42,000 (Party A). Seat 1 → Party A. (Party A updated quotient: 42,000 / 2 = 21,000).
Step 2: Quotients: A = 21,000 | B = 27,000 | C = 15,000. Highest is 27,000 (Party B). Seat 2 → Party B. (Party B updated quotient: 27,000 / 2 = 13,500).
Step 3: Quotients: A = 21,000 | B = 13,500 | C = 15,000. Highest is 21,000 (Party A). Seat 3 → Party A. (Party A updated quotient: 42,000 / 3 = 14,000).
Step 4: Quotients: A = 14,000 | B = 13,500 | C = 15,000. Highest is 15,000 (Party C). Seat 4 → Party C.
Final Allocation: Party A = 2 seats, Party B = 1 seat, Party C = 1 seat. -
Sainte-Laguë Proportional Allocation: Using the Sainte-Laguë divisor method V / (2s + 1), allocate 3 seats in a district where Party A receives 50,000 votes, Party B receives 30,000 votes, and Party C receives 10,000 votes.
Solution:
Initial divisors (2s + 1 = 1): A = 50,000 | B = 30,000 | C = 10,000.
Step 1: Highest quotient is 50,000 (Party A). Seat 1 → Party A. (Party A divisor becomes 2(1) + 1 = 3 → 50,000 / 3 = 16,667).
Step 2: Quotients: A = 16,667 | B = 30,000 | C = 10,000. Highest is 30,000 (Party B). Seat 2 → Party B. (Party B divisor becomes 3 → 30,000 / 3 = 10,000).
Step 3: Quotients: A = 16,667 | B = 10,000 | C = 10,000. Highest is 16,667 (Party A). Seat 3 → Party A.
Final Allocation: Party A = 2 seats, Party B = 1 seat, Party C = 0 seats. -
Hare Quota Calculation (Single Transferable Vote): In a multi-member district electing 5 representatives, 120,000 valid votes are cast. Calculate the Hare Quota Q = Total Votes / Total Seats, and the Droop Quota QDroop = [Total Votes / (Total Seats + 1)] + 1.
Solution:
Step 1: Hare Quota = 120,000 / 5 = 24,000 votes.
Step 2: Droop Quota = [120,000 / (5 + 1)] + 1 = [120,000 / 6] + 1 = 20,000 + 1 = 20,001 votes. -
Wasted Votes and Efficiency Gap Calculation: In a 5-district FPTP election, each district has 100,000 voters (500,000 total). Party X wins 3 districts with 51,000 votes each (losing 49,000 Party Y votes per district). Party Y wins 2 districts with 80,000 votes each (losing 20,000 Party X votes per district). Calculate the total wasted votes for both parties and determine the Efficiency Gap index.
Solution:
Step 1: Calculate Party X wasted votes:
In 3 won districts: 51,000 - 50,001 = 999 surplus wasted votes per district × 3 = 2,997.
In 2 lost districts: 20,000 lost votes per district × 2 = 40,000.
Total Party X wasted votes = 2,997 + 40,000 = 42,997 votes.
Step 2: Calculate Party Y wasted votes:
In 3 lost districts: 49,000 lost votes per district × 3 = 147,000.
In 2 won districts: 80,000 - 50,001 = 29,999 surplus wasted votes × 2 = 59,998.
Total Party Y wasted votes = 147,000 + 59,998 = 206,998 votes.
Step 3: Efficiency Gap = (Party Y Wasted - Party X Wasted) / Total Votes = (206,998 - 42,997) / 500,000 = 164,001 / 500,000 = 0.328 (32.8% severe bias in favor of Party X). -
Rae's Disproportionality Index: A 3-party assembly has the following Vote Share (V) and Seat Share (S): Party A (V = 45%, S = 55%), Party B (V = 35%, S = 35%), Party C (V = 20%, S = 10%). Calculate Rae's Index I = (1 / n) × ∑|Vi - Si|, where n = 3 parties.
Solution:
Step 1: Calculate absolute differences |V - S|:
Party A: |45 - 55| = 10.
Party B: |35 - 35| = 0.
Party C: |20 - 10| = 10.
Step 2: Sum differences: 10 + 0 + 10 = 20.
Step 3: Divide by n = 3: 20 / 3 = 6.67. -
Minimum Winning Coalition Threshold: In a 150-seat parliament (76 seats required for majority), Party A holds 62 seats, Party B holds 40 seats, Party C holds 25 seats, Party D holds 15 seats, and Party E holds 8 seats. Calculate the total seats for the following coalitions and state which qualify as a Minimum Winning Coalition (MWC): (1) A + B, (2) A + C, (3) A + D + E.
Solution:
1. Coalition A + B = 62 + 40 = 102 seats. (Majority achieved; 102 ≥ 76. Not minimal because removing B leaves 62 < 76, but total surplus = 26 seats).
2. Coalition A + C = 62 + 25 = 87 seats. (Majority achieved; 87 ≥ 76. Removing C leaves 62 < 76, removing A leaves 25 < 76. Valid MWC).
3. Coalition A + D + E = 62 + 15 + 8 = 85 seats. (Majority achieved; 85 ≥ 76. Removing E leaves 77 ≥ 76, so E is unnecessary. Not an MWC).
Conclusion: Coalition A + C is the optimal Minimum Winning Coalition. -
Banzhaf Power Index in a 3-Party Assembly: In a 100-seat legislature requiring 51 seats to pass laws, Party A has 48 seats, Party B has 48 seats, and Party C has 4 seats. List all 4 possible winning coalitions (combinations exceeding 50 seats) and calculate the Banzhaf Power Index for Party C.
Solution:
Step 1: Winning Coalitions (Seats ≥ 51):
- {A, B} (96 seats) -> Critical members: A, B (2 critical votes)
- {A, C} (52 seats) -> Critical members: A, C (2 critical votes)
- {B, C} (52 seats) -> Critical members: B, C (2 critical votes)
- {A, B, C} (100 seats) -> Critical members: None (removing any 1 leaves ≥ 52 seats).
Step 2: Total critical votes across all winning coalitions = 2 + 2 + 2 = 6 critical votes.
Step 3: Party C critical votes = 2 (in {A,C} and {B,C}).
Banzhaf Power Index for Party C = 2 / 6 = 1/3 = 33.33%.
(Party C holds 33.33% of real political power despite holding only 4% of parliamentary seats).