MVT and the Political Horseshoe

The polarized American political scene appears to refute the median voter theorem. Joe Rogan once described American politics as a TV show, mocking the radical parties that dominate American legislature. Joe Rogan is irrelevant to this discussion; however, his comment is hilariously true of bipolar American politics. Despite the radical political scene in America, both left-wing and right wing extremists seem to meet in the middle over certain issues in a phenomenon known as the political horseshoe. My question is: can the Median Voter Theorem (MVT) explain the junction of the left and right wing parties?

The MVT requires a one dimensional policy space. Lets assume that the only relevant issue in a political election is the candidates' stance on anti-trust laws, and that all voters exist on a spectrum of weak to strong support for anti-trust laws. Voters are normally distributed, and the median voter distrusts monopolies and would subsequently support legislation to minimize their market power. This is a realistic assumption given YouGov polling data. In this election, there is a far left and a far right wing candidate, and a simple majority vote will determine the election. Since both candidates are vote maximizing, the MVT predicts that far left and the far right politicians will converge on the median voter who supports antitrust laws. In practice we do see strong bipartisan support for antitrust laws. For example, the Sherman Antitrust Act of 1890 received one vote against in the senate passed in the unanimously in the house. 

Its important to note the limitations of this application. The biggest limitation is that political stance on antitrust laws is not the only determinate factor in elections. There are many more issues, and several of them violate the one-dimensionality rule, like immigration. In this case, it may merely be a coincidence that the MVT predicts the convergence of two political parties. Bipartisan support over antitrust legislature may result from aligned party values rather than a fight over the median voter. Regardless, it is still an interesting and important analysis because economic policy has massive implications.

You Can Sell a Whole Neighborhood???

I don't get shocked by a whole lot while I'm catching up on the news, but I did get pretty caught off guard by this proposal: one real estate developer and former HOA president of a neighborhood in Loudoun County, Mital Gandhi, has proposed that himself and his 142 other neighbors should sell their entire neighborhood for data center development. He was a staunch opponent of data center development in Ashburn that has since decided that since data centers have already surrounded their neighborhood and disturb the quietude, residents might as well find a way to benefit. In the proposal, each resident would receive roughly $4.4 million for selling their home to data center developers, which is about double the value of their home. The catch is that this must be a unanimous decision. Getting 143 families to agree to selling their homes, as it turns out, is a tough ask. 

This deal has not gone through yet because of how many holdouts there are. Some families have children that are in school and want to delay the project, and others are emotionally attached to Ashburn, VA. Regardless, because of their emotional attachment to their home, the external cost curve is high. However, the larger problem has been the costs of consensus. Coordination to secure agreement between all 143 families is high. Many holdouts are trying to negotiate a higher piece of the cut for themselves, which adds to the collective cost curve. I would argue that n* in this scenario despite all of the debates is right where it should be for a decision of this magnitude. This has the potential to uproot families at inopportune times and impose very costly externalities on some should it go through without consensus. Unanimity in cases like this ensures Pareto optimality. In the meantime, all residents will continue to hear the pervasive hum of the data centers that currently surround their community. 

Can Your Vote Be Bought?

     Ahead of midterm elections, President Trump has promised all U.S. adults $5,000 if republicans win the midterms, but does being paid $5,000 outweigh the costs of voting? For the sake of this analysis, I will be focusing only on the marginal benefit based on promises, not on the expected future utility stream under each candidate. We know that there is no financial promise being made by other parties running against Trump, so the marginal financial benefit of voting for Trump would be $5,000 for adults. Based on our discussion in class, we also know that the probability of being the decisive vote in Virginia is 1/10,000,000. Using these values, the expected benefit of voting for Trump purely based on the financial promises would be $0.0005, a number that is much lower than the marginal cost of voting. In a different state that historically votes blue, the probability of being the decisive voter is even lower, so the expected benefit is even lower. 
                 While President Trump’s promise seems like a large sum, the expected value for the individual is much lower than the perceived benefit of the offer. If Trump is trying to target people who typically would not vote, this low of an expected benefit might not bring them out to the polls. This number could be swayed, however, if people miscalculate the probability that their vote will be decisive, increasing the perceived value of the promise.
                 On the other hand, we know that people do not always behave predictably when it comes to voting. In terms of straying from the Rational Agent Model, people consistently vote even when the costs of voting exceed the expected benefits of voting. For example, they could have a strong sense of civic duty or be highly influenced by social pressure. In these cases, social pressure could play a major role, especially if people view the $5,000 incentive as being paid out. On a similar note, people who vote for civic duty might be insulted by the offering if they consider their vote something very important that cannot be bought out or they could see the offer as “undemocratic.”

UBE's Mess of an Election

Pursuant to Section 7 Part C of the University Board of Elections Rules and Regulations, student election winners are determined through a Ranked-Choice Voting (RCV) System. The justification for utilizing this system is "to ensure the election of the candidate preferred by the most voters, avoid runoff elections, promote positive campaigning, and encourage greater voter turnout". However, looking at the 2024 First Year Council President Election results may provide evidence challenging the bold claim UBE makes that their system ensures the election of the candidate preferred by the most voters. 

In the 2024 FYC President election, the ballot was initially a First-Past-The-Post, or plurality, system of voting due to a procedural error. In the event that this was the standard voting system of the UBE, Patrick Jo would have been elected the First Year Council President. However, due to the procedural error of the UBE in producing a ballot that was not consistent with the RCV system, they chose to "rectify" the situation by employing an RCV for the top two candidates.

In the pairwise election, I was thus named the successful candidate, demonstrating that Patrick Jo would not have been the Condorcet Winner, as he would not win every head-to-head candidate pairing. However, it is still possible that I was not the Condorcet Winner (and would not defeat every other candidate in a head-to-head vote),  and that the decision to remove all the other candidates from the Runoff Election prohibited voters from revealing their true preferences for another candidate. If the UBE was truly trying to get as close as possible to electing the candidate most preferred by voters, they may elect instead to employ the Borda voting system going forward, which produces the Condorcet winner more often than the RCV system.

Concerning many during this election process was the UBE's decision to rectify their procedural error through a second round of runoff voting between the top two candidates. Prior to the publication of the top two candidates, some candidates felt that the additional time and mental exhaustion costs of a runoff were not worth it, and preferred to simply accept the results of the plurality system of voting, while other candidates wanted to stick it out to have the best possible chance of being elected President. Because a majority decision between candidates to not participate in the runoff election was essentially necessary to convince the UBE not to hold the second round, the majority decision (sticking it out through a second round of voting) imposed costs on the candidates in the minority who were exhausted and preferred not to continue campaigning.

Florida’s Pig-Headed Constitutional Amendment Process

 Since 2006, Florida has required 60% of the vote to amend its state constitution. In most states, the legislature proposes and passes amendments to their state’s governing charter, and then submits the proposal to voters for final approval. And until twenty years ago, Florida was in the vast majority of states which required a simple majority for the enactment of constitutional amendments. Sentiment towards the policy began to shift in 2002, when an amendment passed prohibiting the confinement or tethering of pregnant pigs. Although the sympathy of voters is perhaps admirable, business interests were outraged. The Florida Chamber of Commerce began a campaign to raise the threshold to 60%, arguing that trivial amendments such as these not only “disrespect [the] democratic process,” but also harm underrepresented industries within the state. One swine farmer was awarded $500,000 in damages after the amendment passed, and countless others expressed frustration with the amendment. A referendum to increase the threshold to 60% passed just four years later.

Per the analysis of Buchanan and Tullock, the raised threshold sought to restructure the costs associated with the passage of constitutional amendments. In requiring a supermajority, the model suggests that external costs imposed by these collective decisions on Floridians have decreased, and otherwise affected pig farmers might have avoided the damages imposed by the amendment. In turn, the costs associated with building consensus have increased. Whereas a simple—perhaps naïve—majority might feel sympathy for pregnant pigs, requiring 60% means more expensive advertising campaigns and outreach efforts. Over a million additional Floridians in any given election must be persuaded to vote in favor of proposed amendments, many of whom are potentially negatively impacted (e.g., are pig farmers) and are thus much harder to convince than the first 50% of voters. Although constitutions should be immune to partisan ebb and flow, the failure of amendments which receive 57% of the vote (such as a pro-choice amendment in 2024) have sparked continued debate over the optimal placement of this threshold.

Colombia’s Power-Sharing Democracy

My grandfather often tells me stories of Colombia back in the 60s. One that particularly shocks me is that every four years, when there was an election, everyone already knew which party would win because it was simply its turn. After a decade of partisan violence and a brief military dictatorship, the Liberal and Conservative parties had agreed to stop competing and share power through a pact known as the Frente Nacional. For 16 years, the presidency alternated between the two parties, and Congress, the cabinet, and the courts were split 50/50. Elections still took place, and any citizen could vote, but only candidates from the party on turn could run. The median voter logic didn't disappear; it was constrained. Factions within the governing party had to compete for the whole electorate, so the winner tended to be the candidate closest to the median, but only within that party's ideological range. Voters outside that range abstained from voting, creating a bias and moving the median of actual voters further from the assumed median citizen. 

In the short run, the Frente worked. Before the pact, the two parties were trapped in a prisoner's dilemma: each was better off using violence to capture the state, since holding back while the other attacked meant losing everything, yet mutual violence left both worse off. The power-sharing agreement broke this dilemma and partisan violence fell sharply. But by solving one conflict, the system created a much larger one. Downs argues that new parties emerge when the distribution of voters' ideological views shifts, and existing parties leave part of the space uncovered. Colombia experienced exactly this shift: a growing number of farmers were migrating to the cities, and ideas from the Cuban Revolution and the Soviet Union were arriving through political propaganda, creating a new left-leaning constituency. In a competitive system, a new party would have entered that gap. Since electoral entry was blocked, the entry happened outside the system, through armed movements like the FARC. The Frente ended a partisan civil war, but in doing so it helped lay the groundwork for a new civil war that would last half a century.

Borda Count Voting: 2008 Heisman Case Study

The Heisman Trophy is awarded annually by media voters to the season's most outstanding college football player. Voting is conducted using the Borda Count method; voters rank their top three choices, awarding 3 points for first-place, 2 for second and 1 for third. Generally, this is highly uncontroversial as most years the winner receives an overwhelming majority of the first-place votes. For example, in 2025 Fernando Mendoza received 643 first-place votes while runner-up Diego Pavia received 189. However, the Borda count winner does not necessarily have to receive the most first-place votes. Consider the 2008 voting below:

Tim Tebow received the most first-place votes and finished third, outraging Florida fans and much of the college football-watching public. These fans were shocked by the system, assuming that Tebow would win the award having won a plurality of the votes. Unfortunately, complete ballots are not released publicly and we cannot determine the Condorcet winner for the award. We can clearly see however that Bradford received only 9 fewer first-place votes than Tebow and dominated him in second-place votes by a margin of 108. Bradford had broader support across the rankings, but it would be interesting to check for Condorcet efficiency with full ballot access. Mueller Table 7.4 tells us that in a 3-candidate voting system (oversimplified compared to this case) a Borda Count is 90.8% efficient at selecting the Condorcet winner compared with 79.1% efficiency for plurality voting. While Borda Count voting may seem counterintuitive in the 2008 case, it is likely helpful in the identification of the player with the broadest support.

How redistricting/political gerrymandering can change the median voter: Illinois' 10th Congressional District

Every ten years, the US conducts a population census, and from this census, congressional district lines are redrawn in each state.  In most states, lawmakers in the state legislature draft and pass the new district boundaries just like regular laws. Also, in many of these states, the governor can sign or veto the map. However, if a single political party controls both the state legislature and the governor seat, they can essentially choose the new district lines and control who falls in what district. Naturally, as any rational person/group would, that political party redraws the lines strategically to best ensure their preferences are met. In other words, to have as many candidates of their party as possible in the House of Representatives. When a party redraws electoral district boundaries to give themselves an unfair advantage, it is called political gerrymandering, and even though it seems like it should be illegal, it isn't and happens all the time. So, how do they do this? They take advantage of the median voter theorem. 

Let's say that there is a very competitive two-party district with a normal distribution where the median, decisive voter is extremely moderate, and the median voter might swing either way. Now, imagine the party with absolute control of redistricting, Party A, redraws district lines so that the new district is more in line with Party A than Party B. Now, the median voter favors Party A. One may be thinking that Party B would simply move their ideology toward Party A, but in the real world, the MVT's assumptions do not always hold. Specifically, in the real world, candidates are dealing with many single-issue debates at a time and their mobility on policy isn't as fluid as the MVT states. So, Party A is simply moving the population distribution "closer to them" and almost guaranteeing to win the election.

One real world example that is very personal to me in the redistricting of congressional lines is the 2011 redistricting of Illinois, specifically looking at Illinois' 10th Congressional District. My uncle, former Congressman Robert James Dold Jr., won the 2010 congressional election in a 51.08%/48.92% election in a very competitive race. However, Illinois is an extremely democratic state, and in 2011, Democrats in Springfield proposed a new Congressional map that was drawn without any input from Republicans and was considered to be an attempt to undo the results of the elections held just six months ago. In the redistricting process, not only was my uncle physically forced out of his district, the district was pushed further north into more democratic neighborhoods and removing some of the swing voters that had allowed him to win in 2010. The democrats used the lack of absolute policy mobility to their advantage. They redraw Illinois' 10th Congressional District so that the median voter was now further left on a political ideology scale. Because of this, he was listed as the 5th most vulnerable Republican incumbents in 2012 as a result of redistricting. Even though my uncle was a very moderate republican, he still did not have the mobility to move his political ideology far enough to the left to account for the change of the median voter and in the 2012 election, he lost.

Ranked Choice Fishing

Over Fall Break I got to spend four days floating through Hells Canyon fishing the Snake River and hunting upland game birds in the canyon. On the trip we fished for Smallmouth Bass, Salmon, Rainbow Trout, and White Sturgeon. On the hunting side, we were primarily going after Chukar. At the end of the trip, I asked everyone on the trip which animal they most enjoyed pursuing. The results can be found in Table 1.

Table 1: Animal Preference Chart

	Jarrett	Derek	Omar	Jacob
1	Salmon	Chukar	Chukar	Sturgeon
2	Chukar	Bass	Trout	Bass
3	Sturgeon	Trout	Bass	Chukar
4	Trout	Sturgeon	Sturgeon	Trout
5	Bass	Salmon	Salmon	Salmon

 

With this data, I then analyzed the results using different voting methods to see if there would be any significant differences. Chukar wins in both a plurality and majority + runoff situation. But let’s now look at the results in various ranking systems. Tables 2-4 show the result.

 

Table 2: Results Using the Borda Count

Placement	Animal	Points
1	Chukar	17
T-2	Bass	12
T-2	Sturgeon	12
4	Trout	11
5	Salmon	8

 

Table 3: Results Using Coombs Method

Placement	Animal
1	Chukar
T-2	Trout
T-2	Bass
4	Sturgeon
5	Salmon

 

 

Table 4: Results Using Hare System

Placement	Animal
1	Chukar
T-2	Salmon
T-2	Sturgeon
T-4	Bass
T-4	Trout

 

From all these systems, Chukar was the winner. However, I wanted to see if Chukar is in fact a Condorcet Winner, and Table 5 shows that it is. In a head-to-head matchup, Chukar still beats all of the other options.

 

Table 5: Condorcet Matchup

Matchup	Result	Winner
Chukar vs. Salmon	3-1	Chukar
Chukar vs. Sturgeon	3-1	Chukar
Chukar vs. Bass	3-1	Chukar
Chukar vs. Trout	4-0	Chukar

 

The most interesting part of this is not which animal ended up winning. There was no difference between the methods there. However, it is notable the differences in the order. Most notable is that Salmon came in last in both the Borda Count and the Coombs Method yet secured second place in the Hare System. It demonstrates that the Hare System eliminated the option neither loved nor hated first, while Coombs and Borda got rid of the option most people enjoyed the least. 

Reforming the Downs Framework

    Much has been written about growing political "radicalism" within the West. In the UK, this new "radicalism" has taken shape in Nigel Farage’s Reform and Rupert Lowe’s Restore. If we were to map these two parties using the Hotelling Model, Reform would be to the right of the Conservative Party and Restore would be a little further right of Reform. Within a multiparty system, these parties tend to remain ideologically pure as there is more of an incentive to remain put and secure your base as opposed to moving closer to other party platforms. Downs notes that new parties crop up either as a means to win elections or influence current parties. While it seems as though Lowe’s Restore (2025) was likely founded with the hope of influencing Reform (2021) to move further right to regain the defectors, Reform itself grew out of the Brexit Party. Amazingly, Reform has overtaken the Tories to become the second most popular party in the UK behind Labour. How did this happen?

    According to Downs, parties seeking victory are founded in response to a change in voter distribution or a crisis which disrupts the social order. Because there was no seismic change in voter distribution pre-Brexit, we would conclude that there must have been a crisis which disrupted the social order. For Reform to have surged in popularity in such a short time period is at the very least indicative of the socially disruptive quality of the Brexit decision. To be clear, it would be confirmation bias to use Downs’s framework as a means to retroactively categorize Brexit as a cataclysmic event akin to his examples of WWII or industrialization. Since Downs is rather vague as to defining what it means for a crisis to disrupt the social order, it’s difficult to avoid using confirmation bias to force these events to fit within his framework. Perhaps another explanatory category should be added such as a long run ideological trend. The current trend of populism is arguably the fuel for Reform and many other new parties, and is incredibly difficult to pin down to a single causal event. Adding this new category to the mix could help explain the success of Reform and the rise of other parties that may seem to slip through the cracks of the framework.

Couples, Chaos, and Condorcet Winners

     Contrary to popular American opinion, the most wonderful time of the year is not Christmas, it’s June 1 – the first episode of Love Island USA. My friends and I get together to watch another messy season of couples fighting for the title of America’s Favorite Couple. After the first week, America gets to weigh in on the couples and their compatibility. 

   To vote, viewers register through the Love Island app, where they cast votes on challenges, favorite couples, and potential eliminations. These votes are combined with Islanders’ votes to determine the outcome. When analyzed more carefully, Love Island producers actually implement many different voting systems to answer the various questions they pose to viewers. Sometimes, viewers rank couples from favorite to least favorite, with the couple receiving the most last-place rankings placed at risk of elimination. This resembles the Coombs system. Other times, the couple receiving the fewest first-choice rankings is placed at risk, resembling Ranked Choice Voting. For the final vote, ITV uses a plurality voting system, crowning the couple with the most votes as the winner. 

Determining whether there is a Condorcet winner within these votes is tricky because voters’ preferences are not always fully observable. For example, this season, the Island had a couple, Trinity and Bryce, who appeared to be very strong throughout the process. From an outside perspective, especially in comparison to the other, much messier couples, Trinity and Bryce appeared to be a potential Condorcet winner because viewers could reasonably prefer them over each competing couple in hypothetical head-to-head comparisons. They were ultimately chosen as Season 8’s winners. However, in previous seasons, the plurality winner differed from a potential Condorcet winner. For example, Amaya and Bryan were crowned winners of Season 7. However, their victory was debated by many on social media, with some viewers questioning whether their popularity reflected their true compatibility as a couple. Many argued that Amaya’s popularity as “America’s Sweetheart” contributed to their victory, while stronger couples like Nic and Olandria, may have been more compatible. This commentary suggests that Nic and Olandria may have performed well in a hypothetical head-to-head election against Amaya and Bryan, although this alone would not establish them as the Condorcet winner. Despite this, the actual plurality vote produced a different result, demonstrating how the voting method can influence which couple ultimately wins.

The Right Moment to Enter Politics: The Bulgarian Election Example

Since 2021, Bulgaria has held eight parliamentary elections for government. It became the country with most elections held in the European Union before a permanent council of ministers could be even formed. As a parliamentary republic, the constitution of the state requires a single party or a coalition to have at least 50% of the votes (or seats in parliament) in order to form a cabinet. Except for the last election in April 2026, parties were only able to barely reach 30% of the votes. When majority-rule elections repeatedly fail to produce outcomes that satisfy enough voters, abstention can change the effective electorate and create opportunities for new parties to gain support.

Bulgaria is an interesting example of how different voter turnout can affect election outcomes. If voters become disappointed with their preferred party or candidate and decide not to vote, while supporters of another party continue to vote regardless of who their candidate is, the election result may not reflect the preferences of the population as a whole. This is an excellent opportunity for brand new parties to emerge to capture a larger portion of voter turnout as a group of voters abstain from voting. For example, a party could be preferred by more eligible voters but still lose because many of its supporters stay home while the other party has higher turnout. The absence of duopoly also creates more opportunities for new parties to attract voters who are dissatisfied with the existing parties. In previous Bulgarian elections, a right-wing party gained significantly more votes than the second-largest left-wing party, showing how a party can gain greater representation when turnout is low and its supporters remain more motivated to vote. This asserts that uneven voter turnout can lead to different election outcomes because abstention changes the composition of the electorate, meaning that the median voter among actual voters may differ from the median voter among all eligible voters.

Lawn Selection: Approval vs Borda

    Getting a room on the Lawn is a huge honor but few students know how the winners are actually picked. The lawn selection committee consists of 64 Students. These students vote in rounds: first each member gets a limited number of "yes" votes, then they vote "yes" again on the top 100, and ties are broken by ranking. After the reading, I wondered if instead of approval voting the committee should use a Borda count. During the second round, members would rank every finalist and then add the points rather than a second yes round. The big plus of Borda is that it shows how much a member likes someone, since a "yes" treats a member's first pick and fiftieth pick the same. Mueller reports that Borda picks the Condorcet winner more often than approval, and that it is hard to game.

    The usual problem with ranking is that it takes a lot of effort, but that matters less here because members would only rank the top 100. However, there is a larger problem which is that Borda says the gap between 1st and 2nd is the same as 10th and 11th, which is hard to assume when the qualifications being judged are "meaningful and engaged participation." Along with the time it would take to rank all 100 people, a yes is easier to explain to a student than a rank. Overall, the Lawn's process already works well, but using Borda in round two would make the final cut more precise for a small cost in effort. 

Hotel(ling)

While driving out of Boston Logan Airport to begin my venture home for Fall Break, three hotels made a triangle around I-90: Embassy Suites, Hilton, and Hyatt. With the same multi-story, brown brick, uniform box structure, the buildings' "identity signs" served as their only differentiation. And while the architectural and location choices were identical enough, inside, visitors enjoy all the same complimentary services (breakfast, housekeeping, Wi-Fi, parking) and amenities (gym, pool, mini-fridge, toiletries). The convergence of the greater hospitality industry is explained by, ironically, Hotelling's Spatial Location Theory. 

Each of the three hotels is "midscale." If traveler accommodation preferences were sorted linearly, with camping at 0 and the Four Seasons at 100, Hotelling's Spatial Location Theory predicts market share maximization at this dominating "midscale" tier. The middle-to-high-end travelers sacrificing an infinity pool for a better price point and the middle-to-low-end travelers paying a little extra for a standard pool, for example. And while these hotels might not have a fine dining room, the list of once "luxury" amenities is growing and standardizing (listed above), as brands are forced to match those of their competitors to maintain such market share. The hotel trifecta's location choice (equilateral triangle around Logan) further supports Hotelling's Theory, with all three looking for an even split of traveler demand as travelers flock to the nearest hotel after a long travel day.

Thus, the hospitality industry is unique in that it upholds Hotelling's Spatial Location Theory in the homogenization of both its location and product offerings.

Ranked Choice Chaos in Alaska

Alaskan voters recently affirmed their loyalty to Ranked Choice Voting, and it seems that this decision has the potential to sway a highly contested Senate seat...due to a split vote between current Senator Dan S. Sullivan (R) and retired teacher Dan J. Sullivan (R) who share similar names. Currently, the vote is projected to be neck and neck between Dan S. and Democratic challenger former Rep. Mary Peltola, with Dan J. grabbing just ~3% of the vote. 

However, one Republican interest group filed a complaint with the FEC claiming that Dan J.'s sole purpose in joining the election was to split the Republican vote and bring down Dan S., citing Dan S.'s illegal dealings with ad groups against Dan S. The name confusion is said to be enough to split the Republican vote. However, this is a complaint that rings true with a plurality system of voting like that of Nicaragua, not RCV. Here, the voters leaning towards the imposter Dan J. will almost certainly rank Dan S. as the second option, as a vote for Dan J. seems more like a statement vote than anything more substantial, but yet not enough of a statement to actually vote for a Democrat. 

In this sense, those using this situation to press the iron to RCV have little case. Of course, there is an opportunity to have voters rank Dan J, Peltola, Dan S. and actually split the vote, but this seems unlikely and insignificant (I hypothesize that anyone who votes for Dan J. is on the more extreme side of the political spectrum, and as demonstrated by the Hotelling-Downs Model, will not likely vote for Peltola before Dan S.). Perhaps Alaskans should be grateful for such a voting system that removes the incentives of a vote-splitter, as Dan J. running as an independent in our traditional election systems may actually hold sway (perhaps there is variability in voter preference between the election and the runoff to give an edge to Peltola) and avoid producing the Condorcet Winner.

Are Politicians Still Chasing the Middle Voters?

The Median Voter Theorem suggests that in a two-party, majority rule election, parties will have an incentive to move towards the median voter so that they can get the most amount of votes possible. But what happens when candidates change who the voters are instead?

As politics becomes more polarized and extreme, at least seven states have redrawn their congressional districts to help the party in power prior to the 2026 midterm elections, most favoring Republicans. This process of gerrymandering has reduced electoral competition, meaning that some individuals and groups are losing voting power. It has also created an interesting problem for the Median Voter Theorem. 

Neither the voters nor the candidates preferences have shifted. Instead, the distribution of voters has changed, shifting the location of the median voter and therefore, candidates vote-maximizing strategies. Redrawing the districts moved the median voter closer to the party in power, creating a margin of safety in case of abstention and making it unnecessary for incumbent candidates to moderate their policies. In Louisiana's 6th district, the Black voting population fell from 53% to 25%, shifting the median voter from a liberal to a more conservative voter, reducing the Republican candidate need to appeal to Black voters. 

Politicians are still trying to maximize votes, but by changing district boundaries, they changed the group they need to appeal to. If politicians can choose the voters they need to win, then they may not need to chase the moderate median voter anymore, which can have extreme effects on future elections and the shape of politics as a whole in America.

Is Bolsonaro Brazil's Condorcet Winner?

Condorcet winners seem like an optimist's dream - but finding Condorcet winners in elections is like trying to find a four leaf clover. But could there be one in the Brazil presidential election? Brazil runs its elections as majority rule with a runoff, so since no candidate reached 50% or more of the vote after the recent election results, Lula (incumbent) and Flávio Bolsonaro will be sent to a runoff election. Many of the candidates that received less than 3% of the vote are right of center, so Lula would likely not be the Condorcet winner since Bolsonaro is very right-wing. But does Bolsonaro have the makings of a Condorcet winner? 

There one way this is likely to go when comparing Bolsonaro with any of the minor candidates, including Cury. In an election between Bolsonaro and Cury, if all 47% of Bolsonaro's voters vote for him again, the 53% of other voters decides the election results. Bolsonaro would win the election if he gets a share of non-Bolsonaro voters such that: 47 +53*s > 50 =. s > 3/53=5.7%. Cury would need a share of 94.3% of all non-Bolsonaro voters to win, so it seems like Bolsonaro is a shoe-in for a Condorcet winner. 

To prevent Bolsonaro from becoming a Condorcet winner, 94.3% of all non-Bolsonaro voters would need to vote for Cury. Even though Lula's base is very anti-Bolsonaro, a 90%+ preference for Cury from all non-Bolsonaro voters seems unlikely. Strategic voting could have also caused understatements in the minor candidates' first-round support, which may mean that some Bolsonaro voters engaged in strategic voting and did not vote for Cury even though they liked him. With all that in mind, it still seems like this is a likely case where Bolsonaro is an elusive Condorcet winner.