Any Alaska budget solution will hurt or protect people in four main groups. In any fair solution, all four have to sacrifice.

The state's budget math doesn't work without capping dividends and using Permanent Fund earnings. But we also need an income tax, budget cuts and repeal of oil tax credits. There is no fair solution without a hit to people with each of these interests.

Where you fit in the four-way tug-of-war depends on how much money you make, how old you are, how many kids you have and what industry you work in.

The guy who explained this situation most clearly to me is the only one I've met who seems able to rise completely above it. Cliff Groh, a lawyer who attended Harvard, has been studying Alaska's fiscal and economic situation for decades as a hobby. He gives lectures and has helped put on more than a dozen public forums on the subject. Since May, he has done nothing else, without pay.

He calls the four-way fight the "Groh Square." That name is his nerdy attempt to wring humor out of this dry stuff. He also sometimes lectures in an Abraham Lincoln costume.

But he refuses to give his own opinion. As the chairman of Alaska Common Ground, a small nonprofit dedicated to educating Alaskans about policy choices, Groh speaks only in favor of knowledge.

"What I often call for is for people to actually understand what the choices and trade-offs are, rather than having them assumed," he said.

In Alaska, this is revolutionary talk. We're in the habit of making decisions based on slogans. Groh is asking us to think.

The Groh Square puts the problem in surprisingly simple terms.

The main beneficiaries of Alaska's general fund spending are children, the old and the sick. Health and education departments account for $2.5 billion of our spending. All other agencies combined cost $1.6 billion. Things that can't be cut, including debt service and matching funds for federal construction grants, add $600 million.

So kids and elders hold one corner of the Groh Square.

Low- to moderate-income families hold another corner. The Permanent Fund dividend provides almost a fifth of the income of the bottom half of families. Cutting it slashes their standard of living. Price: $1.4 billion a year.

Upper-income families hold a third corner. An income tax hits wealthier earners harder. It would make a dividend cut fairer. Price (depending on taxes chosen): $200 million to $650 million.

The oil industry holds the final corner of the square. The state's oil tax credits may be inefficient, but the industry supports them as incentives for development. Price: $500 million this year, but going up.

Somehow, those numbers need to cover a budget gap of around $3.6 billion, a deficit that amounts to $4,900 for every man, woman and child in Alaska. Forget about solving it with marijuana taxes, a lottery or other gimmicks. Even if we wanted that many joints and rippies, we couldn't afford them.

I would cap the dividend at around $1,000. It has averaged $1,300 over the last 10 years. Using the rest of the Permanent Fund earnings to pay for government would reduce the budget gap to around $1.5 billion. Taking roughly equally from each of the other three corners would hurt, but it would solve the problem.

Gov. Bill Walker's complex plan takes an hour to explain. But this simple four-way deal is the heart of a fair solution.

To keep the original purpose of the dividend, explained in my last column, it must flow from the Permanent Fund itself at a solid level. But it doesn't need to rise endlessly, and it shouldn't.

We should pay taxes. It's good for us. We've gone long enough with a government that wastes free money. As Gov. Jay Hammond often said, it would be healthier for Alaska to pass out oil money to the public and claw it back through taxes to cover needs that are actually worth paying for.

Imagine the billions we would have saved on boondoggles if we had been paying taxes all these decades. With taxes on money we earn, bloated budgets and excessive oil tax credits would become indefensible as well.

But Groh points out the four corners can gang up against each other more readily than sacrifice jointly. Wealthy income tax opponents team up with education advocates to go after the dividend. Some legislators court oil industry support and pander to dividend recipients to call for cutting services.

On the other hand, sometimes Alaskans do pitch in together. Groh himself volunteers endlessly. When we talked Tuesday, he was spending hours preparing to talk at a 7 a.m. club meeting at a Denny's.

When I asked why he does this work, Groh spoke proudly of his father, who had the same name and was also an attorney, and who helped lead the statehood movement, served on the Anchorage School Board and borough Assembly and in the state Senate.

As a college student, Groh subscribed to both Anchorage daily newspapers by mail. When he came home, he worked as a legislative staffer helping write the 1982 law that gives us the dividend today.

He is a good citizen himself, but the Groh Square illustrates how we respond to our fears. To save our own money or benefits, we're usually happy to cut or tax someone else.

"There's a lot of that going on, in terms of people responding to emotions, their gut responses and their fears," Groh said. "But I always have hopes or I wouldn't keep trying. And I wouldn't have tried so hard over the decades to help people understand really what the facts are, and what the choices are, and have them understand the big picture, and the important details, in terms of what their futures could be like."

Charles Wohlforth's column appears three times weekly. He is the author of more than 10 books, including as-told-to autobiographies of Walter Hickel, Vic Fischer and Dave Rose. Rose's book, which covers the history of the Permanent Fund, is titled "Saving for the Future." Email Wohlforth at cwohlforth@alaskadispatch.com.