There's a saying in New Hampshire that if you live in the Granite State, you have either served as a state representative, are serving now or will serve eventually.

It's an exaggeration, but not by much. Its lower chamber has 400 members in a state of just 1,320,718 residents. That means that in New Hampshire, one out of every 3,302 people is a state representative. Compare that to California, where the state assembly includes just 80 members -- or one for every 475,518 residents. And the current ratio is far from a record in New Hampshire; in the early 1940s, when lawmakers acted to cap the size of the state House at 400, each state representative served a mere 1,230 people.

But the quirks of New Hampshire's governmental architecture -- many of which stem from the 1700s -- don't stop there. Where Granite State governance is concerned, function follows form to an extreme degree.

Take the state Senate. It, paradoxically, is the fourth-smallest in the nation, with just 24 seats, meaning that it takes just 13 lawmakers to stop a bill in its tracks.

The governor, meanwhile, is elected every two years -- a once-common system that now exists only in New Hampshire and Vermont.

There's a five-member, popularly elected "executive council" that acts as a fourth branch of government -- an influential player in state politics, but little understood by the public.

And finally, the state has an electorate courted intensively every four years by presidential candidates, creating a strong interest in politics among voters who remain singlemindedly devoted to maintaining the state's famed aversion to sales and income taxes.

Put it all together and you have the ingredients for a state government like no other, said a range of political observers during recent interviews in the state's largest city, Manchester. New Hampshire politics, they said, is at once transparent and obscure, rigid and unruly, with an unusual degree of checks and balances.

"We've never had a major scandal, there's no widespread corruption and it's pretty transparent," said Tom Rath, a former state attorney general and former Republican National Committee member. "It works, sometimes in spite of itself, but it works. It fits with who we are, and I don't see any great movement for change."

The massive state House is probably the most unique aspect of New Hampshire government, and may have the most profound impact on how politics works in the state.

For example, legislators only get paid $100 a year, meaning that the position tends not to attract careerists. "You see a lot of retirees, or people with job flexibility like realtors or attorneys, or you see college students," said Jamie Burnett, a GOP consultant based in the state capital who previously worked for New Hampshire Republican Sens. Judd Gregg and John E. Sununu, and advised the 2008 presidential primary campaign of Mitt Romney.

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Campaigns also tend to be cheap: Spending $5,000 for a House race would be on the high end of the scale. Some winning candidates can get by with close to zero in expenditures. "It's the opposite of the way it is in most other states," said James M. Demers, a lobbyist in Concord who served three terms in the state House as a Democrat. "Here, you don't have to worry about your ability to fund a campaign, but because of the low salary, you do have to worry about how to support yourself if you win."

The size of the chamber, combined with the low barriers to entry, have had a number of impacts, some positive and some negative. One of the negative ones is that the voters have sometimes elected legislators who have a propensity to offer offbeat opinions.

GOP Rep. Stella Tremblay resigned earlier this year after suggesting that the federal government was behind the Boston Marathon bombing. In 2011, House Republican Martin Harty resigned after he suggested that the mentally ill be sent to Siberia; the 94-year-old had also promoted eugenics as a way to get rid of "defective people."

Democrats have not been immune. In 2010, state Rep. Timothy Horrigan resigned after making a comment on social media that suggested he wished that former Alaska Gov. Sarah Palin had died in the plane crash that killed Alaska's former Republican U.S. Sen. Ted Stevens. (He was later elected twice more to the state House.)

If state representatives can avoid making career-ending gaffes though, the easy entry to the state House can encourage an unusual degree of gender diversity (New Hampshire is more than 92 percent white, so there's little other diversity to be had.) The state's five full-time politicians are all women -- Gov. Maggie Hassan, Sens. Jeanne Shaheen and Kelly Ayotte, and U.S. Reps. Carol Shea-Porter and Ann Kuster. Not all served in the state House, but all benefited from an electorate used to voting for female candidates, observers say.

Ironically, despite the large size of the chamber, it has flipped partisan control three out of the past four elections -- 2006, 2010 and 2012. (The Democrats currently have a 221-179 edge.) "Despite having 400 state reps, almost no one knows who theirs is," said Andrew E. Smith, director of the University of New Hampshire Survey Center. "They vote for 'the Republican' or 'the Democrat.'" This tendency, combined with the existence of multiple at-large seats in some districts, has tended to create waves strong enough to turn even large numbers of seats in one fell swoop.

The difficulty of unifying a large chamber has sometimes enabled unusual cross-partisan alliances. For instance, former two-term House Speaker Doug Scamman, a moderate Republican, was elected thanks to the help of Democratic votes. Meanwhile, a coalition of Democrats and Republicans joined forces earlier this year to oppose Democratic Gov. Hassan's proposal to raise revenue by gambling.

"A body of 400 has so many different factions, it's possible to cut a deal," Demers said. "There are times when the leadership of both parties can lose control of their legislators."

But probably one of the best examples of how the state House informs states politics is the bill process. Whenever a bill is introduced in the legislature -- sometimes numbering up to 1,000 in a single session -- an open public meeting has to be held. "Most states cannot even fathom how do 1,000 open meetings," Demers said. Legislative hearing rooms are booked several days a week, every week, and hearings sometimes run all day long. Every bill has to be voted on and receive a recommendation; if it passes muster in committee and wins approval from the full House, the measure will get a second hearing and vote in the Senate.

While some of these bill hearings are pro forma, others are not. Demers recalls a hearing for a bill that would have added burn coverage to workers compensation.

"The insurance lobby was working overtime to kill the bill," Demers recalled. "One gentleman came in, sat down and told his story about working in a factory. His company was there to clean the walls, and acid sprayed him and burned his body. He had never told this story publicly. There were lawmakers weeping through the whole story, and by the end of the hearing, every committee member was crying with them. Within five minutes it passed, and it's now law."

This role for the general public isn't the only check on government. The structure of the state's governmental branches also prevents anyone from gathering too much power. Indeed, measured by raw power, the governor is one of the nation's weakest, said former state attorney general Rath.

For starters, having a two-year term leaves the governor with almost no time to assemble a record before they need to run for re-election. The most difficult task they face may be putting together a budget, which is traditionally announced in a February address to the legislature. To assemble a budget so quickly requires a governor to lean heavily on agency heads -- officials an incoming governor will not have appointed.

In fact, these agency heads may have spent years securing support on the executive council, the five-member council that must approve all gubernatorial appointments to agencies, commissions and the judiciary, as well as every state contract valued at $10,000 or more. "Quietly, it's one of the most important positions of government in the state," Burnett said. "It's also fair to say it's not very well understood."

Currently, Gov. Hassan is working with a council that has a 3-2 Democratic edge, but prior to 2013, when Democrat John Lynch was governor, it was 5-0 Republican. So every state supreme court nominee Lynch made was a Republican, Rath said.

Meanwhile, if the legislature and the executive council don't conspire against you, the calendar may. "All the substantive agencies are managed by commissioners whose terms are independent of the governor," Rath said. "When a governor takes over, there's very little they can do immediately on forming their own management team. It's one reason we tend to have three-term governors -- it takes four years just to get a hold of the government."

That's why former Gov. John H. Sununu, the senator's father, had to make peace with officials he'd lambasted during his first campaign for governor as not being fit to "run a lemonade stand."

New Hampshire's tight system of checks and balances makes it hard for governors to put their stamp on policy, even when voters give them a mandate.

Part of the reason is the voters' ironclad opposition to both income and sales taxes -- a stance that politicians of either party cross at their own peril. This reality offers elected officials precious few ways to expand revenue, and without additional revenue, broad gubernatorial visions are hard to carry out.

"Citizens here always want government to stay out of the way, and they kind of get what they paid for," University of New Hampshire political scientist Dante Scala said. "Government is small. That helps keep down corruption -- the 'prizes' from being corrupt are small -- but that also means it's difficult to fix problems in the state."

Still, while the design of New Hampshire government has shaped its political destiny for decades, that doesn't mean that it's immune to all change. Recent national trends toward polarization and big money are beginning to have an effect.

Look at campaign finance in the state. In 2012, a Republican Super PAC called New Hampshire Republicans for Freedom and Equality spent at least $240,000 to back GOP legislators who broke with Tea Party aligned, then-House Speaker Bill O'Brien's effort to reverse a pro-gay marriage bill, first in the primaries and then the general election. The group's endorsed candidates did well, though not enough to keep GOP control amid the 2012 Democratic wave.

A bigger impact than the won-lost record, observers say, is that the PAC provided a model for big outside money to play in legislative races that were previously notable for being highly local, low-cost affairs.

"It doesn't cost much money to pay for mailers," Scala said. "If they can do it on that issue, they can do it on others. That could really change the equation going forward."