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Mathematics > General Mathematics
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Computer Science > Computer Science and Game Theory
[Submitted on 15 May 2026] Title:An Axiomatic Theory of Tie-Breaking: Impossibility, Characterization, and Decomposition View a PDF of the paper titled An Axiomatic Theory of Tie-Breaking: Impossibility, Characterization, and Decomposition, by Frank M. V. Feys View PDF HTML (experimental) Abstract:We develop an abstract axiomatic theory of tie-breaking.
McConnell strikes confident tone as midterm elections near
WASHINGTON — Senate Majority Leader Mitch McConnell said Wednesday that it would be a "futile gesture" for a Republican to consider a primary challenge to President Donald Trump in 2020, pointing to his rock-solid standing among the party's base as a significant obstacle. "But everybody’s free to run if they choose to," McConnell said.
Why Murkowski, still opposed, will be marked 'present' on Kavanaugh
More than a 1,000 miles from Washington, wedding bells in Montana on Saturday will cause one Republican senator to change how her vote on Supreme Court nominee Brett Kavanaugh is tallied. Sen. Lisa Murkowski, R-Alaska, said Friday she ultimately will be marked as "present" rather than a "no" when the Senate is expected to confirm Kavanaugh to the nation's highest court. She will be using the "pair between senators" procedure so that Republican Sen.
Confidential FBI report on Kavanaugh handed to White House, Senate
WASHINGTON (NBC) -- The FBI background report investigation on Supreme Court nominee Brett Kavanaugh was handed to the White House and passed on to the Senate overnight, while Senate Majority Leader Mitch McConnell, R-Ky., arranged a key vote on the process for Friday. Copyright 2018 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.
Tensions rise on Capitol Hill as Kavanaugh nomination vote nears
The anticipated vote on Supreme Court nominee Brett Kavanaugh this week has sparked protests and an increased police presence, with small bands of protesters roaming the halls of the Senate office buildings, loudly confronting lawmakers. Multiple senators, including Sen. Susan Collins, who was helped back to her office by Capitol Police after a committee hearing on Wednesday, have been spotted with police escorts in recent days.
How a Kavanaugh Senate vote could play out this week
WASHINGTON — If Senate Majority Leader Mitch McConnell, R-Ky., wants the Senate to wrap up its consideration of Supreme Court nominee Brett Kavanaugh this week, he probably won't be able to wait for the FBI to do the same. “The Senate will vote on Judge Kavanaugh here on this floor this week,” McConnell said on the Senate floor Tuesday morning.
Evidence doesn't support claims against Kavanaugh, Judiciary Committee questioner says
No reasonable prosecutor would bring sexual assault charges against Supreme Court nominee Brett Kavanaugh based on the public evidence, the prosecutor whom Republicans hired to ask the questions during last week's Senate hearing said in a memo to senators.
White House limits scope of the FBI's investigation of Kavanaugh
WASHINGTON — The White House is limiting the scope of the FBI's investigation into the sexual misconduct allegations against Supreme Court nominee Brett Kavanaugh, multiple people briefed on the matter told NBC News.
Senate probing new allegation of misconduct against Brett Kavanaugh
WASHINGTON —The Senate Judiciary Committee is inquiring about at least one additional allegation of misconduct against Supreme Court nominee Brett Kavanaugh, according to a letter obtained by NBC News and multiple people familiar with the process. Republican Senate investigators asked Kavanaugh about the new complaint, NBC News has learned, during a phone call on Tuesday between Kavanaugh and committee staff.
Kavanaugh accuser Ford provides four sworn declarations supporting her allegation
Attorneys for Christine Blasey Ford — who is scheduled to testify Thursday before the Senate Judiciary Committee about her accusations of sexual assault against President Donald Trump's Supreme Court nominee Brett Kavanaugh — have given to committee four sworn declarations from individuals who say she told them of the attack years ago.
McConnell projects confidence but doesn't have the votes for Kavanaugh yet
WASHINGTON — Senate Republicans don’t yet have the votes to confirm Supreme Court nominee Brett Kavanaugh, even as Majority Leader Mitch McConnell is projecting a public face of certainty. “We're going to be moving forward. I'm confident we're going to win. I'm confident he will be confirmed in the very near future,” McConnell told reporters Tuesday afternoon.
Kavanaugh accuser conditionally accepts GOP offer to testify this week
WASHINGTON — Lawyers for Christine Blasey Ford, who has accused Supreme Court nominee Brett Kavanaugh of sexually assaulting her when they were in high school, on Saturday conditionally accepted a GOP offer for her to give Senate testimony this week.
Republicans extended the deadline for Kavanaugh accuser to respond to hearing offer
WASHINGTON — The chairman of the Senate Judiciary Committee on Friday gave the lawyers for the woman accusing Supreme Court nominee Brett Kavanaugh of sexually assaulting her an extension to respond to their counter-offer that would push back the scheduled Monday hearing. But on Friday, just before a 10 p.m. deadline, an attorney for accuser Christine Blasey Ford sent an email to committee staffers requesting an additional day to decide.
Kavanaugh accuser lays out conditions for her to testify about alleged assault
WASHINGTON — Lawyers for the woman accusing Supreme Court nominee Brett Kavanaugh spoke with attorneys for the Senate Judiciary Committee and laid out conditions for her appearance before the panel, including not being in the hearing room with him and assurances that she will be safe.
Kavanaugh preps for Senate testimony on assault allegations
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WASHINGTON — Supreme Court nominee Brett Kavanaugh was back at the White House complex Thursday, amid a week of visits that have included preparation for the possibility of additional Senate testimony, according to a person involved in the confirmation process. In a private session Tuesday, Kavanaugh was grilled by a small group of White House staff about his past, his dating life and his accuser, Christine Blasey Ford's account of events from the early 1980s.
By Rebecca Shabad Verified, Peter Alexander Verified, Leigh Ann Caldwell Verified, Frank V, Marianna Sotomayor Verified
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Aol
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Trump says there's no rush on Kavanaugh vote: 'If it takes a little delay, it'll take a little delay'
WASHINGTON — President Donald Trump said Monday that he is willing to accept that it might take longer to get a vote on Supreme Court nominee Brett Kavanaugh after an allegation that the jurist assaulted a girl while he was in high school surfaced, but added that it was "ridiculous" to ask whether Kavanaugh had offered to withdraw.
McCain's family rips Republican group for using footage of him in ads
The family of John McCain sharply rebuked the National Republican Congressional Committee on Wednesday for releasing political advertisements that use footage of the late senator to attack Democratic candidates in Arizona and Michigan. "The McCain family believes it's unfortunate that the senator's image is being weaponized this election season," a family spokesperson told NBC News in a statement.
Top Democrat refers confidential information about Kavanaugh to federal authorities
WASHINGTON — Sen. Dianne Feinstein, D-Calif., confirmed Thursday that she had referred information about Supreme Court nominee Brett Kavanaugh to “federal investigative authorities.” “I have received information from an individual concerning the nomination of Brett Kavanaugh to the Supreme Court. That individual strongly requested confidentiality, declined to come forward or press the matter further, and I have honored that decision.
John McCain's family slams GOP group for using footage of him in ads
The family of John McCain sharply rebuked the National Republican Congressional Committee on Wednesday for releasing political advertisements that use footage of the late senator to attack Democratic candidates in Arizona and Michigan."The McCain family believes it's unfortunate that the senator's image is being weaponized this election season," a family spokesperson told NBC News in a statement.
John McCain's family slams GOP group for using footage of him in campaign ads
The family of John McCain sharply rebuked the National Republican Congressional Committee on Wednesday for releasing political advertisements that use footage of the late senator to attack Democratic candidates in Arizona and Michigan. "The McCain family believes it's unfortunate that the senator's image is being weaponized this election season," a family spokesperson told NBC News in a statement.
Abusive calls are the latest in a pressure campaign against Sen. Collins
WASHINGTON — The campaign of pressure on Sen. Susan Collins, R-Maine, to oppose the confirmation of Supreme Court nominee Brett Kavanaugh has escalated to include vulgar phone calls, shipments of wire hangers sent to her office and a questionable high-dollar fundraising drive against her that her office likens to extortion. As a potential GOP swing vote, Collins has been at the center of attention for both parties since President Donald Trump announced Kavanaugh's nomination in July.
McConnell says close Senate midterm races like 'a knife fight in an alley'
WASHINGTON — Senate Majority Leader Mitch McConnell said Tuesday that the Senate races in this year’s midterm elections are going to be “very challenging,” comparing each one to “a knife fight in an alley.” Speaking to reporters at the Gene Snyder Federal Courthouse in Louisville, Ky., the Kentucky Republican was asked if Republicans will hold onto the majority in Congress. “We know this is going to be a very challenging election,” he said.
Senate to hold hearing allowing Kavanaugh and his accuser to testify publicly
The Senate Judiciary Committee will hold a public hearing next Monday in which the woman who’s accusing Supreme Court nominee Brett Kavanaugh of sexually assaulting her when they were both in high school will be able to testify, and Kavanaugh will have the opportunity to respond. “As I said earlier, anyone who comes forward as Dr. Ford has done deserves to be heard.
Proposal to rename Senate office building after McCain stirs backlash
WASHINGTON — The death of Sen. John McCain has sparked a new debate in the Senate over how best to honor his legacy, and a proposal to rename a Senate office building after the late Arizonan is threatening the rare bipartisanship that has been on display in Washington since his passing. Senate Minority Leader Chuck Schumer on Monday proposed that one of the three office buildings that house senators and their staffs — the Richard Russell Senate office building — be renamed to the John S.
GOP downplays latest Trumpworld legal woes as Dems call for Kavanaugh delay
Republican lawmakers on Wednesday argued that the conviction and guilty pleas of two former Trump aides are not a major congressional concern because they are not related to allegations the campaign colluded with Russians, while Democrats said the president's implication in a crime should result in a delay in confirmation hearings for his Supreme Court nominee.
National Archives: All requested Kavanaugh documents probably won't be released until the end of October
WASHINGTON — The National Archives said Thursday that it will not be able to complete a GOP congressional request for documents related to Supreme Court nominee Brett Kavanaugh’s work in the White House until the end of October, which could drastically affect the timeline for his confirmation.
Democrat leader calls on George W. Bush to release Kavanaugh documents
WASHINGTON — Senate Minority Leader Chuck Schumer is ramping up Democrats' efforts to obtain documents involving Supreme Court nominee Brett Kavanaugh by asking former President George W. Bush to release mountains of files from the judge's time in the White House.
Schumer calls on Bush to release Kavanaugh White House documents
WASHINGTON — Senate Minority Leader Chuck Schumer is ramping up Democrats' efforts to obtain documents involving Supreme Court nominee Brett Kavanaugh by asking former President George W. Bush to release mountains of files from the judge's time in the White House.
Senators remain frustrated over family reunification efforts after briefing
WASHINGTON — Senators from both parties remained doubtful about the administration's ability to reunify more than 2,500 separated families, and skeptical that the "zero tolerance" policy will not be resurrected, following a closed-door briefing on Capitol Hill by administration officials.Senators left the briefing frustrated at the lack of answers by a handful of administration officials, saying they were given no guarantee that every child separated from their parent would be...
Reaction to Trump: 'Shameful,' 'treasonous,' 'disgraceful'
President Donald Trump was swiftly rebuked by lawmakers, TV anchors and pundits across the political spectrum Monday after his joint news conference in Finland with Russian President Vladimir Putin.Sen.
Progressive group launches ad campaign urging Democrats to oppose Kavanaugh
WASHINGTON — A progressive group working to sink President Donald Trump's Supreme Court nominee is launching its first round of advertising Friday in three key states to pressure Democratic senators to vote against Brett Kavanaugh. Demand Justice is spending a portion of its $5 million budget on the ads aimed at Sens.
No clear path forward in Congress to end family separations
Nearly two months into the implementation of the policy at the border, congressional members are sounding the alarm and vowing to find a solution as images of mothers being torn from their children permeate the news. The issue poses a significant challenge to a Congress that has been unable to pass any significant immigration legislation for nearly 30 years. And the urgency has grown as Republicans fret about a backlash from midterm voters in less than six months.
Trump on defense as Congress pushes back on tariffs
WASHINGTON — President Donald Trump is working to head off a confrontation with members of his own party on trade, personally reaching out to senators to express his opposition to legislation that would tie his hands on tariffs. On Wednesday morning, Trump called Sen. Bob Corker, R-Tenn., to say he opposed the senator's introduction of legislation that would give Congress oversight of tariffs. Corker said that he listened, but declined to drop the push. “I’ve got a job to do," he said.
Agriculture Department Proposes Bioengineered Food Disclosure Standard | JD Supra
On May 4, the Agricultural Marketing Service (AMS) of the U.S. Department of Agriculture announced a proposed rule to establish a national disclosure standard for foods that may contain bioengineered ingredients.
Hatch apologizes to McCain for slamming his no-Trump funeral plans
Sen. Orrin Hatch, who called it "ridiculous" that Sen. John McCain would not want President Donald Trump attend his funeral, apologized to his ailing GOP colleague Tuesday for the off-the-cuff remark. Hatch, a Nevada Republican, sent a private apology letter to his Arizona colleague, Hatch's office confirmed. News of the apology was first reported by The Washington Post.
Hatch apologizes to McCain for slamming his no-Trump funeral plans
The senator's daughter, Meghan McCain, said earlier Tuesday on ABC's "The View" that people criticizing her father needed to relax. "I would like everyone to take a collective breath and chill out on my dad for a second, especially Orrin Hatch," she said. People close to McCain, who does not want the president to attend his funeral, have informed the White House the plans do not call for Trump to be there, a source told NBC News.
Senate Foreign Relations Committee backs Pompeo's nomination after last-minute reversal by Sen. Rand Paul
"Having received assurances from President Trump and Director Pompeo that he agrees with the President on these important issues, I have decided to support his nomination to be our next Secretary of State," Paul tweeted. At the White House, Trump said, "I heard Rand Paul went yes...he’s a good man. I said he’d never let us down.
Senators vote to allow babies on Senate floor
WASHINGTON (NBC) — Newborns will now be allowed on the Senate floor after senators voted unanimously Wednesday to allow infants under the age of 1 added to the short list of people who can enter the exclusive area. The request to change Senate rules was made by Sen. Tammy Duckworth, D-Ill., who was the first sitting senator to give birth. She gave birth to Maile Pearl Bowlsbey on April 9. There were practical reasons for the request.
Senators vote to allow babies on Senate floor
WASHINGTON — Newborns will now be allowed on the Senate floor after senators voted unanimously Wednesday to allow infants under the age of 1 added to the short list of people who can enter the exclusive area. The request to change Senate rules was made by Sen. Tammy Duckworth, D-Ill., who was the first sitting senator to give birth. She gave birth to Maile Pearl Bowlsbey on April 9. There were practical reasons for the request.
Corker praises the Democrat who wants to replace him
WASHINGTON — Sen. Bob Corker, R-Tenn., isn't running for re-election but he had many words of praise Wednesday for the Democratic candidate who is trying to replace him. Phil Bredesen, the former Democratic governor, is running in a tight race against Republican Rep. Marsha Blackburn for the open Tennessee senate seat. Corker has donated money to Blackburn but said he won't campaign against Bredesen.
Kucinich's ties to Syria's Assad roil gubernatorial fight for Ohio Democrats
With just three weeks left to go in Ohio’s gubernatorial primary, the state’s last Democratic governor is warning that one of his own party’s candidates for the job is tied to “some of the most despicable people imaginable,” saying Democrats will lose if they nominate him. Former Gov. Ted Strickland tore into Dennis Kucinich after financial disclosures showed that a group tied to Syrian dictator Bashar al-Assad paid the former congressman $20,000 for a speech last year.
Top of the (Capitol) Dome to ya (w/ @lacaldwelldc & @mariannaNBCNews)
Top of the (Capitol) Dome to ya (w/ @lacaldwelldc & @mariannaNBCNews) Top of the (Capitol) Dome to ya (w/ @lacaldwelldc & @mariannaNBCNews) - Spherical Image - RICOH THETA
Congress faces old gun debate with new pressure to act
WASHINGTON — Congress Monday started grappling with how to move forward on the issue of gun violence as they returned to Washington for the first time since the shooting at Marjory Stoneman Douglas High School. They began going through the motions of what has become a familiar ritual in the wake of horrific mass shootings in recent decades, one marked by emotional rhetoric and no legislative action.
Prospects of new bipartisan DACA agreement remain uncertain
WASHINGTON — As the Senate struggles to find an immigration bill it can pass, two new bipartisan proposals are being rolled out, both containing some of President Donald Trump’s demands but parting dramatically on others. The fate of those plans was clouded even before their release as the president issued a warning to Republican senators Wednesday to support his proposal, which was introduced as a bill by Sen. Chuck Grassley, R-Iowa.
White House chief of staff John Kelly: Dreamers won't be targeted for deportation
WASHINGTON — The White House chief of staff said Tuesday that "Dreamers" would not be a priority for deportation, even if their Obama-era protections expire and a deadlocked Congress hasn't completed a deal to protect them. John Kelly told a small group of reporters at the Capitol that as long as an immigrant in the U.S. illegally has no criminal record, they are likely to stay "out of anyone's scope" for a long time. "They are not a priority for deportation," he said.
Searches spike for MS-13 as Trump makes gang a focus
Search interest in the MS-13 gang spiked during Trump's address, according to stats released by Google. The president told a story of two young teenage girls who were murdered by members of the gang, as well as touted the bravery of a Homeland Security agent who recently commanded an operation that Trump said resulted in the arrest of more than 220 MS-13 members.
Democrats react to Trump immigration remarks
If you’re happy with yourself and you know it, clap your hands. The anti-Trump Twitterverse exploded with criticism Tuesday night after State of the Union viewers noticed that the president was repeatedly clapping for himself. While it is customary for lawmakers in attendance at a State of the Union address to applaud after the commander in chief delivers lines they agree with, it isn't typical for the president himself to consistently applaud himself along with the audience.
Fact check: Trump overstates tax relief for middle class
If you’re happy with yourself and you know it, clap your hands. The anti-Trump Twitterverse exploded with criticism Tuesday night after State of the Union viewers noticed that the president was repeatedly clapping for himself. While it is customary for lawmakers in attendance at a State of the Union address to applaud after the commander in chief delivers lines they agree with, it isn't typical for the president himself to consistently applaud himself along with the audience.
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