The Mathematics of Electoral Fragmentation: How Guyana’s Voting System Rewards Unity

Mathematical Realities: How Electoral Fragmentation Benefits the PPP/C in Guyana’s 2025 Election

As Guyana approaches its September 2025 general election, the opposition landscape continues to fragment in ways that underscore a fundamental truth about the country’s electoral system: unity matters more than politics—it’s about mathematics.

This week’s resignation of Amanza Walton-Desir from the People’s National Congress Reform (PNCR) and the launch of her new political movement, Forward Guyana, marks yet another splintering of an already divided opposition. Her departure follows the collapse of coalition talks between A Partnership for National Unity (APNU) and the Alliance For Change (AFC), reinforcing a pattern that is accelerating at precisely the moment when unity matters most.

With just four weeks remaining until Guyana’s July 14 Nomination Day, this analysis examines how the country’s proportional representation system creates structural advantages for unified political blocs over fragmented ones, using objective mathematical principles to demonstrate why the People’s Progressive Party/Civic (PPP/C) stands to benefit significantly from opposition disunity.

Understanding Guyana’s Electoral Mathematics

Guyana employs a list proportional representation system for electing its 65-member National Assembly, featuring several distinctive characteristics that reward consolidation over fragmentation. The system allocates 25 seats across 10 geographic regions while distributing 40 seats from national “top-up” lists. Crucially, it uses the Hare Quota with largest remainder method and, unlike many proportional systems worldwide, has no minimum percentage requirement for parties to qualify for seats.

The Hare Quota is calculated by dividing total valid votes by available seats. In 2020, with 460,352 valid votes and 65 seats available, each seat required 7,082 votes. However, the mathematics of seat allocation becomes significantly more efficient when votes are concentrated in fewer parties rather than dispersed across many.

The Fragmentation Penalty: A Mathematical Demonstration

Consider a hypothetical regional example that illustrates this principle clearly. In a region with 5 seats and 50,000 valid votes, the Hare Quota would be 10,000 votes per seat.

Scenario A: Unified Opposition

• PPP/C: 26,000 votes (2 full quotas + 6,000 remainder)
• United Opposition: 24,000 votes (2 full quotas + 4,000 remainder)

Initial allocation gives each bloc 2 seats, with 1 remaining. Since PPP/C has the largest remainder (6,000), it receives the final seat. Result: PPP/C 3 seats, Opposition 2 seats

Scenario B: Fragmented Opposition

• PPP/C: 26,000 votes (2 full quotas + 6,000 remainder)
• Opposition Party 1: 12,000 votes (1 full quota + 2,000 remainder)
• Opposition Party 2: 8,000 votes (0 full quotas + 8,000 remainder)
• Opposition Party 3: 4,000 votes (0 full quotas + 4,000 remainder)

Initial allocation gives PPP/C 2 seats and Opposition Party 1 just 1 seat. The two remaining seats go to the largest remainders: Opposition Party 2 (8,000) and PPP/C (6,000). Result: PPP/C 3 seats, Opposition Parties combined 2 seats

While this simplified example shows identical outcomes, the real disadvantage compounds across multiple regions and through the national allocation system.

Regional Arithmetic and Effective Thresholds

The fragmentation penalty becomes more severe in smaller regions. In a single-seat region with 20,000 votes, if PPP/C receives 9,000 votes (45%) while three opposition parties receive 4,000, 3,600, and 3,400 votes respectively, PPP/C wins despite 55% of voters choosing opposition candidates.

This mathematical reality reflects a broader principle: smaller regions create higher effective thresholds for winning seats, and unified parties can more easily surpass these thresholds than fragmented ones competing for the same voter base.

Historical Evidence: Unity vs. Fragmentation

The 2020 election demonstrates near-perfect proportionality when opposition forces remained unified. The PPP/C received 233,336 votes (50.69%) and won 33 seats (50.77%), while the APNU+AFC coalition received 217,920 votes (47.34%) and won 31 seats (47.69%). This 1:1 vote-to-seat conversion reflected the mathematical efficiency of having two large, unified blocs.

Contrast this with elections featuring greater fragmentation. In 2006, the PPP/C won 54.6% of votes but secured 56.9% of seats—a 2.3 percentage point bonus. In 2011, the PPP/C won 48.6% of votes but secured 50.8% of seats—a 2.2 percentage point advantage. These disparities directly resulted from opposition vote dispersion across multiple parties.

The 2025 Mathematical Landscape

With the AFC-APNU split confirmed and new parties like Forward Guyana entering the race alongside existing smaller parties such as Change Guyana and A New and United Guyana (ANUG), the opposition faces increasingly complex mathematical headwinds.

The former APNU+AFC coalition’s 47.34% vote share from 2020 will now be divided among at least two parties, with neither likely approaching the PPP/C’s unified total. Each additional party further dilutes opposition efficiency in converting votes to seats through several mechanisms:

• Quota inefficiency: Smaller parties struggle to accumulate full quotas in regional allocations
• Remainder disadvantage: Multiple small remainders lose to fewer large ones in final allocations
• Regional threshold effects: Fragmented parties fail to reach effective thresholds in smaller regions
• National amplification: Regional inefficiencies compound through the top-up system

Beyond the Mathematics

While this analysis focuses purely on mathematical realities, it’s important to acknowledge that electoral politics involves considerations beyond arithmetic efficiency. Voters and parties must balance these structural factors against ideological alignment, governance philosophy, and the democratic value of diverse political voices.

However, for opposition parties concerned primarily with electoral success, the mathematics are unforgiving. Guyana’s proportional representation system—designed to ensure fairness—paradoxically creates structural advantages for unified blocs over fragmented ones.

The Narrowing Window

As Nomination Day approaches, Guyana’s opposition faces a fundamental choice between mathematical pragmatism and political principle. The electoral arithmetic suggests that without serious consolidation efforts around common candidates, platforms, and strategies, September’s outcome may be determined not by public sentiment or campaign effectiveness, but by which political forces best understood and adapted to the mathematical realities of electoral survival.

The 2020 election demonstrated what’s possible when opposition forces unite: near-perfect proportional representation. The question for 2025 is whether opposition parties will learn from this mathematical lesson or allow fragmentation to deliver structural advantages to the PPP/C that no amount of campaigning can overcome.

In electoral politics, as in mathematics, some equations have predictable solutions. Guyana’s opposition now has four weeks to decide whether to solve for unity or division.