Republicans go to the polls Tuesday, March 8, in Michigan, Mississippi, Idaho and Hawaii. Democrats vote in Michigan and Mississippi. This post will provide news, analysis, exit polls and results throughout the day.

Update (March 9, 7 a.m. PT): Final results

Tuesday winners

Michigan: Donald Trump (37%), Bernie Sanders (50%)

Mississippi: Donald Trump (47%), Hillary Clinton (83%)

Idaho: Ted Cruz (45%)

Hawaii: Donald Trump (42%)

What it all means

Donald Trump: The businessman and reality-TV star once again has a big night, and once again shows that no matter what attacks are thrown at him, his supporters stick with him. He is well on his way to winning the Republican nomination -- on the first ballot.

Ted Cruz: With his victory in the Idaho primary, the Texas senator solidifies his place as the chief alternative to Trump, likely setting up a head-to-head battle down the home stretch.

John Kasich: The Ohio governor earns a strong second place in Michigan, giving him some momentum heading into his home state's primary. He still hasn't won a contest and is pinning his long-shot hopes on a contested convention.

Marco Rubio: The Florida senator has another disastrous night. He's trailing badly in the polls in his home state. It's hard to see how this campaign ends well for him.

Hillary Clinton: The Democratic front-runner grabs a comprehensive win in Mississippi, but her shock loss in Michigan points up her vulnerabilities, making party insiders who are looking toward the fall a little nervous.

Bernie Sanders: The insurgent Democrat proves on Tuesday that he can win in a big, diverse state -- and that he's more than a single-issue candidate. He has the money and the passionate support to go all the way to the convention -- and maybe, just maybe, beyond.

Update (March 8, 8:50 PT): Sanders wins Michigan

Former Secretary of State Hillary Clinton has been trying to pivot to the general election for the past two weeks, but Vermont Sen. Bernie Sanders isn't letting her. Sanders' insurgent campaign, calling for a "political revolution," scored its biggest victory so far by topping Clinton in Michigan. Sanders has now proved he can win a primary in a big, diverse state with his anti-establishment message. The victory holds the potential to alter the race's narrative, showcasing the strength of Sanders' agenda and forcing Clinton to redouble her efforts to win over the liberal base of the party.

It also highlights Clinton's vulnerabilities. She remains mistrusted by some 60 percent of Americans, thanks to more than two decades of Republican vitriol and suspicion directed at her and her husband, former President Bill Clinton. The incessant drip-drip-drip of the email scandal from her tenure as secretary of state will continue to drag on her image.

So now Clinton and Sanders look to March 15, when Florida, Illinois, Missouri, North Carolina and Ohio vote. Perhaps at the end of those elections, one of the Democratic presidential candidates will be able to pivot toward the general election.

Update (March 8, 6:10 p.m. PT): Trump triumphant again

Donald Trump has won the Michigan primary. It looks like Ohio Gov. John Kasich will take second place, giving him at least some momentum heading into his home state's primary next week.

Trump said tonight that increased Republican turnout from the 2012 primaries is the "biggest story in politics right now." His point being that he has brought the new blood into the party. He has affirmed once again his status as the GOP front-runner, fending off Ted Cruz in two more important contests. Even if Cruz ends up winning the Idaho primary, the night will belong to Trump. March 15 will offer up a last stand for Kasich and Marco Rubio, if not for Cruz, but at this point it looks like Trump is on a glider path to his party's nomination.

Update (March 8, 5:45 p.m. PT): Convention or bust

Ohio Gov. John Kasich and Florida Sen. Marco Rubio have talked a fair amount about a contested Republican convention, largely because that's essentially the only way either of them could end up as the nominee. To have a shot at that goal, the two candidates almost certainly have to win their home states, which both vote on March 15. If they do, the possibility of an open convention will start to feel real to Republican insiders. "Among GOP elites," writes the Washington Post, "the only agreed-upon mission is to minimize [Donald] Trump's share of the delegates to enable an opponent to mount a credible convention challenge."

But Trump isn't the only candidate who opposes this scenario. Texas Sen. Ted Cruz wants Kasich and Rubio out of the race so he can face Trump head to head.

"Any time you hear someone talking about a brokered convention, it is the Washington establishment in a fevered frenzy: they are really frustrated because all their chosen candidates, their golden children, the voters keep rejecting," Cruz said last week, playing to the anti-establishment fervor that has fueled both his and Trump's campaigns. "So they seize on this plan of a brokered convention, and the D.C. power brokers will drop someone in who is exactly to the liking of the Washington establishment. If that would happen, we would have a manifest revolt on our hands all across this country."

Depending on the final results tonight, Trump and Cruz could soon get that head-to-head match-up they desire. Rubio will finish in single digits in Mississippi. His vote tally in Michigan could be nearly as disastrous. Steve Schmidt, John McCain's chief strategist during the 2008 presidential election, said on MSNBC this evening that the Florida senator has "a tough decision to make" about continuing in the race.

Kasich, on the other hand, is hoping to sneak into second place in Michigan, setting him up for Ohio next week.

Update (March 8, 5:30 p.m. PT): Clinton, Trump win

Hillary Clinton has won the Mississippi Democratic primary by a "significant" margin, multiple news sources project. Donald Trump has won the Mississippi Republican primary, sources project. Ted Cruz will finish in second place.

Update (March 8, 4:30 p.m. PT): Trump's new torture laws

Donald Trump has faced increased criticism of his views on torture. So he's begun to moderate his stance -- a little bit.

"We're going to stay within the laws," the real-estate developer now says. "But you know what we're going to do? We're going to have those laws broadened."

What does that mean? Trump has said many times that the U.S. should be undertaking methods "a hell of a lot worse" than waterboarding, the largely discredited interrogation technique that makes a prisoner feel as if he or she is drowning. Ariz. Sen. John McCain, the 2008 Republican presidential nominee and a POW during the Vietnam War, has said "waterboarding is an affront to all of the standards that we believe in and adhere to of humane treatment of people."

Update (March 8, 3:30 p.m. PT): Early exit polls

Anger remains the driving factor for many Republican voters, according to early exit polls compiled by ABC News. This is good news for insurgent candidates Donald Trump and Ted Cruz.

Michigan GOP voters angry at the federal government: about 40 percent

Mississippi GOP voters angry at the federal government: about 30 percent

In Mississippi, 84 percent of Republican voters describe themselves as evangelical Christians.

Democratic voters in Mississippi were asked who "they would trust to handle race relations." Here's how an early sampling answered in exit polls:

Only Hillary Clinton: 47 percent

Only Bernie Sanders: 11 percent

Both of them: 35 percent

Neither of them: 4 percent

They were also asked whether the candidates should continue President Barack Obama's generally middle-of-the-road Democratic agenda. Here's how voters responded, which could be good news for Clinton:

Continue Obama's policies: 72 percent

Change to more liberal policies: 20 percent

Change to less liberal policies: 6 percent

In Michigan, Democratic voters were asked whether they found the candidates "honest and trustworthy." Here's how they responded:

Hillary Clinton: about 60 percent

Bernie Sanders: about 80 percent

Update (March 8, 2:45 p.m. PT): Medgar Evers brother backs Trump

Mississippi has a troubled racial history, epitomized perhaps most famously by the 1963 assassination of civil-rights leader Medgar Evers and the murders the following year of three civil-rights workers traveling through the state. (The 1964 killings were the inspiration for the fictional 1988 movie "Mississippi Burning.") So what do Mississippians think about how Donald Trump's campaign has drawn some white-supremacist support, leading to the "Racists for Donald Trump" sketch that "Saturday Night Live" aired over the weekend (watch below)? That's hard to say, but here's something we do know: Medgar Evers' brother endorsed Trump this week.

"I believe in him first of all because he's a businessman," said Charles Evers, Medgar's 93-year-old brother. "I think jobs are badly needed in Mississippi."

Evers, who served as Mississippi field secretary for the NAACP and mayor of Fayette, Mississippi, became a Republican in 1980. His opinion of Trump's views on race? "I haven't seen any proof of him being a racist," Evers told the Clarion-Ledger newspaper. "All of us have some racism in us, even me."

Update (March 8, 1:45 p.m. PT): Sanders' last, best hope?

USA Today says Michigan is "Bernie Sanders' last, best chance to challenge Hillary Clinton's hold on the Democratic presidential race."

That's because it's big, offering a whopping 130 delegates. And because Democratic voters in the struggling rust-belt state should be receptive to Sanders' message on income inequality and his outside-the-political-mainstream prescriptions. Sanders calls for government-run single-payer health insurance, making public colleges tuition-free, expanding Social Security and reestablishing the Glass-Steagall Act that separated investment and commercial banking.

Offers Susan Demas, publisher of Inside Michigan Politics: "If he can't win in Michigan, where can he win besides these small caucus states?"

A Sanders victory in the Wolverine State, where the Vermont senator has been trailing in the polls, certainly would knock Clinton back on her heels and possibly change the race's narrative. But even if Sanders loses in Michigan, he's not going away. He continues to raise impressive amounts of money and has said he plans on fighting all the way to the convention no matter what happens.

Update (March 8, 1:05 p.m. PT): Why Bloomberg stayed out

Want to know why former New York City Mayor Michael Bloomberg decided against launching an independent campaign for the presidency?

The media baron, a Republican with liberal views on most social issues, considered running chiefly to prevent GOP front-runner Donald Trump from reaching the White House. But as polling savant Nate Silver indicates with the electoral-vote map below, a Bloomberg campaign likely would have hurt the Democrats far more than the Republicans.

Update (March 8, 11:35 a.m. PT): The end of the GOP?

Republican insiders fear they are witnessing the destruction of their party, and they could be right. The two major parties have been adept at survival -- taking on new positions as times change, fighting off the worst ideas of their fringe elements. But major parties have disappeared before in this country. The Grand Old Party itself was born from the ashes of the 19th century Whigs -- the party of President William Henry Harrison, iconic Senator Henry Clay and Abraham Lincoln's Secretary of State William H. Seward.

There's no denying that businessman and reality-TV star Donald Trump is changing the GOP as he brings out voters who don't typically support Republicans or usually don't even vote at all. Expanding a party's voter base is generally seen as a good thing, but exit polls show that in Trump's case the new voters tend to be nihilistic: they feel betrayed by the major parties and are angry at government and elected officials.

Trump's nativist appeals, as has been widely documented, also draw supporters who are even more objectionable to mainstream Republicans than incumbent-haters. Huffington Post reporters Ryan Grimm and Julia Craven point out that the Trump campaign is serving "as a welcoming committee of sorts to new racists hoping to enter the party."

Trump's rivals, meanwhile, want to woo at least some of the reality-TV star's voters. Texas Sen. Ted Cruz and Ohio Gov. John Kasich have repeatedly said they understand the frustration and fury of voters drawn to Trump and can provide solutions for them. And Florida Sen. Marco Rubio says his overwhelming win in Sunday's Puerto Rico primary "is evidence I can take conservatism to people who don't normally vote Republican."

March 8 election preview (6:30 a.m. PT): Trump makes 'electability' case

"A normal Republican cannot think of bringing in Michigan, and if you don't bring in Michigan, it's tough," Donald Trump said at a rally in the Wolverine State this week. "You have a very narrow road. But I'm going to bring in places like Michigan."

The Republican presidential front-runner is talking about the general election in the fall. The controversial businessman and reality-TV star has focused on his electability in the run-up to Tuesday's contests in Michigan, Mississippi, Idaho and Hawaii. He's had to, because over the weekend his rivals -- benefiting from various attacks on Trump including the late-night comedy show "Saturday Night Live" airing a mock "Racists for Trump" ad -- scored some momentum. Texas Sen. Ted Cruz beat Trump in Kansas and Maine. And Florida Sen. Marco Rubio, dismissing calls from Trump and Cruz to get out of the race, won convincingly in the territory of Puerto Rico.

So Trump has begun playing down (a little bit) the nativist appeals that have stirred outrage and talk instead about how he's the Republican presidential candidate most likely to best former Secretary of State Hillary Clinton, the Democratic Party's front-runner.

But he's not only relying on the "electability" issue. With Michigan the big prize on Tuesday, he also insists he will restore the U.S.'s manufacturing glory by dropping a 35-percent tariff bomb on U.S. companies that move factories overseas. Many economists believe this kind of big-time trade tax, assuming Trump could get it through Congress, would be disastrous, setting off a trade war that would blight the houses of all involved. But never mind that. Trump says the threat of a tariff is all that would be needed. Within a day or two of issuing the warning, Trump says, any CEO who was planning to shift production out of the U.S. would call him up at the White House.

"They'll say: 'Mr. President, we're moving back. Would you like us to move to Michigan?'" Trump said. "I'll say, 'Yeah, I really want you to move to Michigan.' And they'll move back."

Such outcomes might indeed be nothing more than a demagogic fairy tale Trump is spinning, a shout-out to the angry, disaffected voters who have fueled his campaign. But he's undeniably onto something important here. Income inequality -- and government's inability to do anything about it -- is a key part not just of the insurgent campaign Vermont Sen. Bernie Sanders is waging for the Democratic nomination. It's central to Trump's as well on the GOP side. Trump's most dedicated supporters, the think-tank Rand Corporation found, are those who answer yes to the following survey question: "People like me don't have any say about what government does."

In short, people increasingly believe that, whether a Republican or a Democrat is in the White House, the rich get richer and, thanks to corrupt politicians in Washington, D.C., the rest get the shaft.

That's why some Democratic insiders are agitating for Clinton to pick Massachusetts Sen. Elizabeth Warren as her vice president -- assuming, that is, Clinton is able to see off Sanders' primary challenge. Warren, the first head of President Obama's Consumer Protection Bureau, was the left's hero before Sanders launched his long-shot presidential campaign. (Indeed, liberal groups last year made a concerted effort to get her to join the race for the White House, but she demurred.)

Democrats on Tuesday go to the polls in Michigan and Mississippi, with Sanders trying to tamp down talk of Clinton's nomination being inevitable. Clinton leads Sanders 55 percent to 42 percent in the final Michigan polls, but Sanders is trending up. In the final Mississippi polls, Clinton holds a commanding lead -- up by some 40 percentage points in some surveys.

As for the Republicans, Trump led the final Michigan polls -- generally in the 30-36 percent range -- with Cruz and Ohio Gov. John Kasich trailing in the low 20s. Trump appears to have significant leads in Idaho and Mississippi.

Kasich is the lone Republican still in the race who has yet to win a contest. But he's looking to gain late momentum for the March 15 primary in his home state by pulling a surprise in Michigan. Playing up his blue-collar roots, he believes he can cut into Trump's base. "If they can hear me, and what I've done, that's the ticket," he said this week. "I believe that if I can sit with some Trump people -- I won't get them all -- if I can sit with them, they're going to understand that I'm one of them."

-- Douglas Perry