## A Twin Paradox Variant, With a Surprise

The “Twin Paradox” in Special Relativity is well known.  One of  the pair, conventionally Homer, remains on Earth while his twin, Ulysses, takes off in a high-speed rocket for another star, rounds the star and comes home.  When Ulysses emerges from his spacecraft he finds that Homer has aged far faster than he has.  A naive reading of SR holds that Ulysses could have considered himself stationary, while Homer moved at high speed, and therefore Ulysses should have aged faster, and that is the paradox.

The answer is that the roles of the twins are not symmetric: Homer remained in a single frame of reference, while Ulysses changed his frame of reference with at least three accelerations, and the age measurement is taken in Homer’s unchanged frame of reference.  Every detailed calculation shows that the “paradox” disappears when this is taken into account.

But a friend recently came up with a variant on this, where the roles of the twins were symmetric.  Suppose, he said, that Homer and Ulysses blasted off in opposite directions at the same speed, turned around after a set time, and then returned.  As they approach each other on the return, each sees the other’s clock as running more slowly than his own.  So when they pass each other, which is older?

The answer is that each sees the other’s clock as running more quickly than his own, but, amazingly, when they meet both find that they have aged the same amount!  The analysis follows here, and is encapsulated in this Spacetime Diagram

If you aren’t familiar with a spacetime diagram, the x axis is space, the t axis is time.   Lines are the motion of objects, their so-called “worldlines”.  The scale is such that the speed of light is 1; lines which are at 45o (slope = 1) are light rays. Lines with slope $m>1$ are the paths of objects moving at velocity $v=\frac{1}{m}$.

In this diagram, the red lines are the path of Homer’s Rocket, and the green lines are the path of Ulysses’ rocket.   The black lines are light rays sent between the ships.

The diagram is always drawn in some frame of reference.  In this case, I’ve chosen a frame of reference which moves along with Homer’s rocket on its outbound journey.

There are some text notations on the diagram.  Beside each colored line segment is a notation of the form $\tau=kt$, for some $0.  This gives the value of  the proper time  $\tau$ for a ship on that line  as a fraction of the time $t$; the proper time is just the time kept by a clock moving on the ship.

Beside the light rays are the values for the Doppler Shift of the light rays: the difference in frequency from the source to the observer.  When $D(v)=2$, the light rays have twice the frequency at the receiver that they had at the source; when $D(v)=0.5$, they have half the frequency.  It’s important to note that the Doppler shift affects every periodic phenomenon: in particular, it affects clock ticking.  When the Doppler Shift is 2, the observer will see clocks ticking twice as fast as the person at the source sees them.

For completeness, we should give the formulae for these things.  When two objects are approaching with velocity $v$, $D(v)=\sqrt{\frac{1+v}{1-v}}$.  When they are receding with velocity $v$, $D(v)=\sqrt{\frac{1-v}{1+v}}$.  The formula for $\tau$ is also simple: $\tau=(\sqrt{1-v^2})t$.

Now that that’s in place, we can describe the experiment.  Homer and Ulysses blast away from each other at 60% of light speed: $v=0.6$.  After one year of proper time ($\tau$, not $t$), they turn and blast towards each other at $v=0.6$.  At all phases of their journey, they agree to flash lights every second, so each can keep track of the proper time on the other’s ship.  The total number of light flashes each sends is the total proper time on that ship.

Their journey is the red and green parallelogram in the diagram, which is the spacetime diagram as seen from an observer who moves in the direction of Homer’s ship as it moves away from Ulysses’ ship.  When Homer makes the turn, the observer doesn’t.

We start out at the bottom.  From $x=t=0$, the ships blast away from each other.  Since the observer starts out moving with Homer, in the observer’s frame Homer is motionless but Ulysses is blasting away at $v=0.6$, represented by a line with slope $-5/3$.  We can see that Homer’s proper time is just $t$, but Ulysses’ proper time is $0.8t$ — according to the observer, Ulysses’ clock is running slow.  Homer and Ulysses, meanwhile, are exchanging light signals (say one per second) but the Doppler Shift is 0.5 — they are receiving light signals at the rate of one every two seconds.  According to each, the other’s clock is running at half-speed.  At $t=1$, Homer’s $\tau,\tau_H=1$, so Homer makes the turn: Ulysses, however, keeps blasting away until $t=1.25$, at which time Ulysses’ $\tau,\tau_U=1$.  Once this happens, Ulysses is now co-moving with the observer (his velocity is the same as Homer’s original velocity), so from the perspective of the observer Ulysses is now motionless and Homer is blasting towards Ulysses at 60% of the speed of light, so now $\tau_U=t,\tau_H=0.8t$.

For the first part of this epoch, Homer is seeing light from Ulysses that left Ulysses’ ship while it was moving in the same direction that Homer’s ship is now.  As a result, there is no Doppler shift, and Homer and Ulysses both see the other’s clock as keeping perfect time.  This lasts until the light ray that left Ulysses’ ship at Ulysses’ turn reaches Homer’s ship, which is when $t=x+2=-5/3x+1$, or $x=-3/8,t=13/8$.  Homer’s proper time at this point is $12/8$.   The Doppler shift is now 2, so each of  Homer and Ulysses think the other’s clock is moving twice as fast as  his own.  This continues until they pass, at which time each sees the other’s clock is moving half as fast as his own.

However, if they stopped and compared clocks, they would each see that the same proper time had elapsed for both of them; if they counted flashes received vs sent, they would see that they had sent the same number of flashes.  In fact, if they exchanged one flash every tenth of a year (proper time), they would each report that during the first year of their journey, they sent 10 flashes and received 5; over the next six months, each sent 5 and received 5; and during the final six months, each sent 5 and received 10.  Each would report that the proper time of his journey was 2 years, and each sent and received 20 flashes.

Now (for the sake of completeness) let’s consider how an observer in the original frame of reference (the one Ulysses and Homer inhabited before they left) saw both journeys.  If Homer and Ulysses had relative velocity $s$, each had velocity $v$ from the perspective of an observer in the original frame of reference, where $s=\frac{2v}{1-v^2}$.  A little algebra shows $v=\frac{1-\sqrt{1-s^2}}{2s}$, and plugging in $s=0.6$ we get $v=1/3$  So from his perspective, Homer and Ulysses each blasted away at 1/3 of the speed of light for $1/\sqrt{1-(1/3)^2}=1.06$ years, turned, and returned at the same rate.  According to him, both were gone 2.12 years, while Homer and Ulysses each saw the journey take 2 years exactly.

## Stopping Trump For Certain

There is a reasonable chance that Mr. Trump will get a majority of delegates on the first ballot at the Republican convention.  It is generally assumed that this guarantees him the nomination: majority election is interwoven into our political fabric so tightly we assume that it is a fact of nature.

Well, it isn’t.  It’s a rule of each party: in the case of the Republican Party, it’s Rule 40(d) of the Republican Party Rules.  And these rules can be, and are, modified at each convention.  There’s been lots of speculation that the RNC would modify Rule 40(b) to permit individuals that hadn’t won eight states to be placed in nomination.  If they can do that, they can raise the threshold for nomination.

So how much should they raise it?  One reasonable target is 2/3 of the delegates, or, this year, 1650 delegates.  This was actually the standard for the Democratic Party from 1832-1936, when it was abolished at the time of the unanimous renomination of FDR.  Interestingly, the rule had been suspended in 1836 and 1840, only to be reinstituted to prevent the renomination of President Martin van Buren.   It’s worth noting that every Republican nominee since 1976 easily passed the 2/3 threshold, and in the postwar years only Eisenhower (1952), Richard Nixon (1968), and Gerald Ford (1976) won on the first ballot with less than 2/3 of the vote.

It is still mathematically possible for Mr. Trump to win 2/3 of the delegates; only 734 delegates to date are committed against him, and it would take 825 to keep him from a 2/3 majority.  If he runs the table on the remaining primaries, he could do it.

Now, should the GOP stop him this way?  Of course they should: Mr. Trump is not an acceptable candidate for President of the United States, or the leadership of any major Democracy.  He has disqualified himself through his unceasing threats of lawlessness and violence.  This has nothing to do with his policies or ideology, or, frankly, lack of same: it has everything to do with his behavior.  His behavior and rhetoric would have had him censured or expelled from any legislative body; recused from any bench, and likely impeached; fired for cause as an executive with any public corporation.  Should a political party have lower standards than that?  Of course not; the simplest and most direct solution would be to just refuse to permit him to have his name placed before the convention.  Failing that, at least require him to get a supermajority.

## Justin’s Amazing Poem

It’s hard to overemphasize Justin Trudeau‘s overwhelming victory on Monday night. While neither the percentage of the vote (39.47%) nor his percentage of seats won (54.44%) were very remarkable, it represents a turnaround without equal in the history of Canadian politics — and, as nearly as I can tell, the history of advanced democracies.

And then Trudeau, dismissed as handsome and pleasant but lightweight, pulled off one of the most remarkable campaigns in the history of advanced democracies. Consider the numbers:

• Trudeau increased his party’s vote from 18.91% of the vote in 2011 to 39.47%, an increase of 20.56% of the vote. This easily the largest increase for an existing party in Canada’s history; only the Mulroney landslide of 1984 (17.58%), the Diefenbaker landslide of 1958 (15.17%) and the 2011 rise of the NDP (12.45%) were in double digits.
• This is only the second time in Canadian history that a third-place party became the largest party in the next election, and the only time that a third-place party has formed a majority.
• This is only the third time in the last eighty years that a majority government of one party has been replaced by a majority government of another party, and only the fifth time over that span that a majority government has lost at all.
• Trudeau increased his share of House seats from 11.04% of the seats to 54.44%, an increase of 43.4%. Once again, this is a record for Canadian elections. Only Mulroney in 1984 (38.30%) and MacKenzie King in 1935 (34.29%) even come within 10% of Trudeau’s triumph.
• Trudeau’s freshman class — MP’s who first won election in 2015 — is so large that it would easily be the largest party in the House. In fact, it’s bigger than three minority governments (1962, 1972, 2006) and very close to two more (1957, 2004).

Those data speak to the historic magnitude of Trudeau’s victory.  No party leader in Canada has ever increased his party’s share of the vote or seats by anything like as much as Trudeau did.  Comparisons are often made to his father‘s 1968 victory — the “Trudeaumania” election.  But that was in fact quite modest — Pierre  Trudeau added a modest 5.19% of the vote and 8.9% of the seats to the 1968 Liberals’ pre-election totals,  compared to his son’s 20.56% of the vote and 43.4% of the seats.  But more impressive was the efficacy of his campaign.  Historical data to compare to other leaders are not available here, but it’s hard to imagine a campaign that had a more significant effect.

According to the authoritative ThreeHundredEight.com, the Liberals started the campaign in third place with 25.9% of the vote, compared to the NDP’s lead with 33.2% and the Conservatives’ 30.6%.  The Liberals managed to increase their vote total marginally, to about 29.6% of the vote, by Sept. 20, while the NDP declined slightly to 29.8%.  But then there was a decisive break — over the last month of the campaign the Liberals added about 10% support while the NDP dropped 11%.  Effectively, Trudeau persuaded about one-third of NDP supporters to vote for him instead.

Now that’s impressive.  Part of the credit surely belongs to Prime Minister Harper, who inspired a depth of antipathy that led to at least some strategic voting.  Though there have been many news reports of the “Anyone-but-Harper” movement, I haven’t seen any quantitative analysis of its effect.  Part of Mr. Trudeau’s massive victory was surely momentum; some percentage of those who switched from the NDP to the Liberals in October were motivated by the fact that Mr. Trudeau had the best chance to unseat Mr. Harper.  Some of his gains  from the NDP in Quebec, too, were surely due to the niqab affair;  even Quebec NDP candidates opposed NDP leader Thomas Mulcair’s principled stand that Muslim women should be permitted to wear the traditional face covering when taking the oath of Canadian citizenship.  However, Mr. Trudeau used the issue as the centerpiece of a thoughtful speech on individual liberty and collective responsibility, which I recommend reading.

Still more impressive is Mr. Trudeau’s popularity.  It’s a common experience in politicians that the day they are nominated (or, in the case of a Canadian political leader, elected to the leadership) is the peak of their popularity.  Indeed, that was the case for Mr. Trudeau, up until yesterday.  Liberal popularity peaked at 38% just after his election as leader, and then declined, more or less steadily, until the start of the campaign.  Then, as noted above, it leveled and then began a continuous rise until election day, where he peaked at 39.47%.

An analysis of his success would be worthwhile, and will come later.  And governing is not campaigning — as New York Governor Mario Cuomo observed, you campaign in poetry and govern in prose.  Of course one doesn’t know Mr. Trudeau’s skills as an essayist.  Today, however, we can observe he has written a marvelous poem.

## And Then There Were Four…Andre Iguodala Joins The World’s Most Exclusive Club

Three years ago, Alvin AuYoung and I pointed out that  Shaquille O’Neal held all three major championships in basketball: the NBA Championship, (2000, 2001, 2002, 2006), the Olympic Gold Medal (1996), and the FIBA World Cup (1994).   We incorrectly said that he was, at the time, the only member of Basketball’s Triple Gold Club: David Robinson had the 1986 World Cup, the 1992 and 1996 Gold Medals, and the 1999 and 2003 NBA Championships.  Less than a month after we wrote the piece, Tyson Chandler added the 2012 Olympic Gold Medal to his  2010 FIBA World Cup Championship and 2011 NBA Championship.  Now there’s a fourth: with the Golden State Warriors victory over the Cleveland Cavaliers last month, Warriors’ Sixth Man Andre Iguodala added the 2015 NBA Championship to his 2010 FIBA World Cup Championship and his 2012 Olympic Gold Medal.

Iguodala’s march to the triple gold was similar to Shaq’s.  Shaq won the 1994 World Cup while a member of the Orlando Magic, the 1996 Gold Medal after his last season with the Magic, and the 2000 NBA title with the Lakers.   Iguodala won the 2010 World Cup while a member of the Denver Nuggets and the 2012 Gold Medal after his last season with the Nuggets.  Both were Finals MVPs in their first NBA championship.  Shaq was younger (28 at his triple gold while Iguodala was 31).

Though there are now only four members, they had better make room for more.  Both of the Splash Brothers,  Klay Thompson and Stephen Curry, have both the  2015 NBA Championship and the 2014 World Cup Championship, and are locks for the US team in the 2016 Summer Olympics.  In fact, Curry has two World Cups, from 2014 and 2010.  Curry would have joined  the club with Iguodala,  except that he was prevented from playing in the 2012 Olympics because of a knee injury.

While Thompson and Curry seem to be locks, others are knocking on the door.  Kevin Love has both a Gold Medal and a World Cup Championship, and the Cavaliers are likely to be strong contenders next year.  Kevin Durant, Russell Westbrook,  Anthony Davis, and James Harden also are only missing the NBA Championship.  Kyrie Irving needs both an NBA Championship and a Gold Medal, but given his near-certain selection to the US team next year and the Cavaliers’ strength, he could win both the Gold Medal and the Larry O’Brien trophy in a single year.  LeBron James heads a list of great players (Kobe Bryant, Dwyane Wade, Chris Bosh, Tayshaun Prince) with both a Gold Medal and an NBA Championship, but he won’t have an opportunity to complete the Triple until 2019.  At that point he’ll be 35, and may not want to play international basketball.

Similarly, Manu Ginobili has a 2004 Gold Medal to go with his four NBA Championships (2003, 2005, 2007, 2014), but in 2019 he’ll be 42, and, realistically, Argentina is a longshot.  So this looks to be an exclusively American club for a number of years.

## Obama’s Community College Idea Should Get GOP Support

I haven’t annoyed my Republican friends for some time, and I’ve been kicking my Democratic friends in the shins, so it’s time to restore a little balance.  President Obama’s Community College idea is a good one, and it should be supported.  And even Prof. Milton Friedman (might) say it’s a good idea.  Here’s why.

Here’s why.  Friedman proposed a college financing proposal in which a student sold equity in himself to the government.  It’s summarized here, but the net is really simple: the student gets a grant to attend school, and in return promises to pay a proportion of his income to the government.  In effect, he’s sold stock in himself to the government.

Great idea.  But we already have such a program.  It’s called the income tax.

Now, I am not a huge fan of the income tax.  It’s basically a tax on work, saving, and investment, and if you tax anything you get less of it.  That’s why we have sin taxes on booze and cigarettes; we’re trying to discourage their consumption.  I don’t like the income tax because I don’t want to discourage work, saving, and investment.  But that said, we have it, and it’s not going away anytime soon.  If you net it out, community college graduates earn about 1/3 more than high school graduates.  About 20% of that accrues to government through taxes.  That pays for the cost of college, many times over, and is thus an exceedingly good fiscal bet.  In effect, the income tax acts as Prof. Friedman’s equity collector — with zero transactions costs.

## #DeflateGate culprit? Physics

PV = nRT.  It’s one of those laws you learned in high-school physics.  For any gas, pressure x volume = number of molecules x temperature.  The New England Patriots’ balls were tested in the Referee’s Room before the game.  We don’t know the temperature, but 70°F = 20°C = 293.5°K is a good guess.  The temperature dropped into the low 40’s (275°K or so) during the game.  That’s a drop of about 6% from testing conditions, and so — you guessed — pressure would also drop by 6%.  The Patriots say that they inflate the balls to 12.5 psi, the minimum allowable under the rules.  That’s above ambient pressure of 15 psi, for a total of 15 + 12.5 = 27.5 psi.    6% of 27.5 is about  1.65 psi, so a drop in temperature alone explains a reading of  11.1 psi.   ESPN reports the actual number as 11 psi, so that’s it.    Physics did it.

## All in, The Unbalanced Schedule Wasn’t That Unfair

The 2013 Major League season is (almost) over, with only a tiebreaker playoff between the Tampa Bay Rays and the Texas Rangers remaining.  But the complaints have been flying fast and furious that the Major League schedule for 2013 was unfair to teams in the American League East.  Specifically, contending teams from the West and Central divisions were able to fatten up on relatively weak opponents (Houston, Seattle, the White Sox, Minnesota) while the AL East was strong top-to-bottom.  Since the wild card is a competition among teams from all divisions, the claim is that in a balanced schedule the AL East teams would have been far more competitive for the two wild-card spots.  See, for example, http://msn.foxsports.com/mlb/story/unbalanced-schedule-unfair-al-east-teams-wild-card-race-092213 for a representative complaint.

Interesting thesis: but is it true?  To find out, we calculated the Balanced Schedule Equivalent Record for major league teams.  The BSER calculates what team’s records would have been had the Major Leagues played a balanced schedule in 2013.

The logic behind the BSER is simple: each team played a total of 142 games against the 14 other teams in its own league, plus 20 interleague games.  This works out to an average of just a little over 10 games against each team in a balanced schedule, as opposed to 19 games against teams in its own division and an average of 6.6 games against teams in the other two divisions.  If we scale each head-to-head record by the appropriate factor (142/(19*14) for teams in one’s own division; 142/(6.6*14) for teams in the other divisions) we arrive at what the in-league record would have been for each team, had they played a balanced schedule.  Add in the interleague games, and, voila; we have the final BSER.

The results for the National League are shown in Table 1

Team BSER Wins Actual Wins
LA Dodgers 97.83413078 92
St. Louis 97.56504899 97
Atlanta 94.48849396 96
Cincinnati 92.28844839 90
Pittsburgh 91.04198916 94
Washington 83.27080108 86
Arizona 82.23747789 81
San Diego 77.39849624 76
Milwaukee 76.40145819 74
NY Mets 73.71747551 74
San Francisco 69.66860626 76
Chi Cubs 69.4157176 66
Miami 61.11854544 62

Though there are some differences here (LA finishes with the National League’s best record, instead of having the third seed, and Pittsburgh goes to Cincinnati for the wild card instead of the other way round), the playoff teams are unchanged.  In the American League this is (almost) true as well.

Team BSER Wins Actual Wins
Boston 97.52548651 97
Oakland 96.24581214 96
Cleveland 91.35019367 92
Tampa Bay 90.27956254 91
Detroit 89.38933271 93
NY Yankees 88.68694463 85
Baltimore 88.61631351 85
Kansas City 83.01655794 86
LA Angels 82.45823198 78
Texas 81.26986123 91
Toronto 77.72932331 74
Seattle 68.79630142 71
Minnesota 68.04830257 66
Chi White Sox 66.44679882 63
Houston 49.00820232 51

Boston keeps the league’s best record, and Oakland remains the #2 seed, a game behind. Interestingly, Cleveland actually wins the Central by two games over Detroit, and Tampa Bay is the other wildcard.  The complaints do have some validity: Texas did benefit enormously from the unbalanced schedule, winning 10 games more than they would have done in a balanced schedule.  However, the AL East teams wouldn’t have done a great deal better under a balanced schedule (Tampa Bay would actually have lost a game, and the Yankees and Baltimore would only have picked up three each).

The calculation here is quite simple; if Major League baseball is genuinely perturbed by this season’s outcome, it could shift to the BSER to calculate wild-card teams and home-field seedings for the playoffs, thus permitting MLB to retain the unbalanced schedule and the excitement of the division races while maintaing fairness in inter-division competitions.

Or not.  The flaws in that plan are easy to see from the above tables: the whole point of unbalanced schedules is to emphasize division games.  Suppose a team finished second in its division in the unbalanced schedule, but third in the wild-card race behind the third-place team in its own division (as you can see from the above, the BSER can invert standings in a division).  Who goes to the wildcard?  And should Cincinnati or Pittsburgh have the home-field this year?  Pittsburgh finished ahead in the division, but Cincy in the BSER race…

## The World’s Most Exclusive Club

[This is written jointly with Alvin AuYoung]

What’s the NBA’s Most Exclusive Club?  Well, let’s first consider this question in the context of other sports. The Club should honor specific, noteworthy achievements, and have very few members.  The Club of Golf Grand Slam Champions might qualify: a purist would argue that the only member is Bobby Jones, but with four straight Grand Slam Championships across two years, Tiger Woods might also be considered a member.

But we do know of one high-achievement club with only one member, and it’s very likely that it will contain only one until June of 2013: the Basketball Triple Gold Club.   Who’s the member?  Well, that’s the trivia question…but, first, we should describe the Basketball Triple Gold Club.

The Basketball Triple Gold Club consists of people who have won all three of basketball’s most prestigious tournaments: the NBA Championship, the Olympic Gold Medal, and the FIBA Basketball World Cup.  It’s modeled on the Hockey Triple Gold Club,  which features the winners of the Stanley Cup, the Olympic Gold Medal, and the IIHF World Championship.  There are 25 members of the Hockey Triple Gold Club: nine Canadians, eight Russians, six Swedes, and two Czechs, and  the hockey world does take it very seriously.

But the Hockey Triple Gold Club has a large, and unavoidable, element of bogusness to it: the IIHF World Championship resembles college basketball’s NIT more than anything else.  It’s held annually, and it is held at the same time as the Stanley Cup playoffs.  As a result, it features mostly players who couldn’t make the NHL, or whose teams missed the playoffs, and occasionally a few stars whose teams got knocked out in the first round.    Players whose teams perennially go deep in the NHL playoffs are unlikely to ever participate in the IIHF World Championship, so there’s a large element of luck involved in even playing in the tournament.

Who’s the Mystery Member?

The Basketball Triple Gold Club is not nearly as inherently suspect: the FIBA World Cup is held quadrennially, and doesn’t conflict with the NBA season.  The world’s best could, if they wanted to, show up every fourth year to play for their country.  And, typically, unless the players are Americans, they do.  However, in 1998 NBA players were barred from playing in the FIBA World Cup due to that season’s NBA lockout, and in 2002 a number of NBA stars skipped the FIBA World Championships.    The shocking sixth-place finish of the US in 2002 and its bronze medal in the 2004 games reinvigorated America’s commitment to international basketball, and it’s possible that the FIBA World Cup will attain the stature in basketball that the World Cup does in soccer.    Barring injury, no top soccer player would miss the FIFA World Cup, and no top European player would miss the UEFA European Championship.

OK, enough suspense: who’s the guy?  The sole member of  the Basketball Triple Gold Club is Shaquille O’Neal, and, yes, that noise you hear in the background is Kobe Bryant‘s teeth gnashing.  O’Neal won the 1994 FIBA World Championship, four NBA Championships, and an Olympic Gold Medal in 1996.  Kobe has five NBA championships and an Olympic Gold from 2008, but has never been on a FIBA World Cup champion.

The Sole Member of the Triple Gold Club

So who’s likely to join Shaq?  The only possibility at the Olympic Games this year is Pau Gasol.  Gasol has a FIBA World Championship (2006), and two NBA titles (2009, 2010, Lakers).  The only other NBA/FIBA champions are  Peja Stojakovic of Serbia (FIBA champions, 2002) and, recently, the Dallas Mavs (NBA champions, 2011), Lamar Odom  (World Cup, 2010; NBA Champion, 2009, 2010), and Chauncey Billups (World Cup, 2010; NBA Champion, 2004). But Peja has retired and Serbia didn’t qualify for the Olympics this year, Billups is unable to play until December with a torn Achilles and  Odom wasn’t named to the Olympic team.

Shaq might get company before too long, though.  The US are heavy favorites in London, and if they do bring home the  gold five members of the team will have both FIBA World Championships (from 2010) and Olympic Gold Medals — Kevin Love, Kevin Durant, Tyson Chandler, Russell Westbrook and Andre Iguodala; and the smart money is that an NBA title is in the future for at least some of these young and rising stars.  So Shaq might have company as early as June of 2013.

The next opportunity will be at the FIBA World Cup of 2014, and a number of the game’s greatest could have a shot then, if they want it: Kobe Bryant, LeBron James, Dwyane Wade, and Chris Bosh, (for the latter three, Gold Medal 2008, NBA Championship 2012), to name four.  Manu Ginobli has a Gold Medal (2004) and three NBA Championships (2003, 2005, 2007)  to his credit, and so long as he plays Argentina has a live chance.  He turn  37 in 2014, however, and has been a professional since 1995.

## The National Popular Vote System

In the previous three posts, we’ve introduced the Threshold Popular Vote, showed how it would work in practice, and compared it to other electoral college reforms.  In this post, we’ll look at the simplest of all reforms: dump the electoral college and elect the President directly.  It’s good enough for most countries with a Presidential system; it’s good enough for the 50 states when they elect governors; the electoral college is an 18th century artifact that was a sop to the slaveholding South (James Madison, in fact, wanted popular election, but Southern states feared the popular election of a Northern abolitionist); we’ve gotten rid of our previous forms of indirect election (the US Senate was elected by state legislatures until the ratification of the 16th Amendment); the US is a much more homogenous nation now than it was in 1789, so we don’t need to protect regional interests; and so on.

All correct.  But so what?  There are two variants of the National Popular Vote: a Constitutional Amendment, which is a reasonable idea that will never pass, and the National Popular Vote Compact, a terrible idea that just might pass.  We will consider both of these here.

## The National Popular Vote Amendment

The only really reliable way to abolish the Electoral College is through a Constitutional Amendment, which requires the ratification of 3/4 of the states: in other words, 13 states can block an amendment.   And the current system favors the small states, and there are at least 13 small states who will never, ever ratify such an amendment.  Why should they?  Currently, 189,000 Wyomingans select one elector: 683,500 Californians do.  A Wyoming resident has roughly 3.5 times the voting power of a California resident, and simply won’t give it up.

In fact, it never gets that far: Congress has only once gotten a Presidential popular vote amendment out of committee, and it never passed the House.   In general, there is a minor flurry of activity after each close election, and then it dies out. Unless and until there is some reason to believe that the popular vote will overcome the political hurdles that have many times stayed it, this remains a dead letter.

There is another, more subtle and tenuous objection. The United States has two Federal institutions explicitly designed to ensure representation of minority regional interests: the Senate and the Electoral College. Further, despite its original design as a weak federation of strong states, the United States has evolved into a continentwide strong federation of weak states, with a relatively low level of regional tensions. Contrast this with Canada, designed as a strong federation of weak provinces, but without any real Federal institutions designed to protect regional interests (the Canadian Senate is a toothless sinecure for political appointees, and is strongly biased to Eastern and Central Canada: the six provinces east of the Lakehead have 78 Senators; the four to the west, 24). Canada has evolved into a weak Federation of strong provinces, with persistent centrifugal tensions. Of course there are other factors, such as the minor matter of the Civil War. That said, the lessons of Canada, and the European Union’s current difficulties, is that one cannot have a strong central government in a federation without central institutions designed for regional representation.

The logistical objection to the National Popular Vote is the probability of a national recount.  Elections in the United States are exclusively state and local elections; there is no national election, nor any means to administer one.  Even the presidential election, which we think of as a national election, is in fact 50 simultaneous state elections plus an election in the District of Columbia.    There are some common rules, by Constitutional law by statute: universal suffrage, national age of eligibility to vote, federal oversight over electoral districts, limits on campaign spending.  The Constitutional requirement to choose all electors “on the same day” probably requires all states to hold their election on a common date.    But places and times of voting, the actual ballot, ballot access, counting procedures, recount thresholds and procedures, are all under state control.  It was a state official, Florida Secretary of State Katherine Harris, who certified Governor Bush’s win over Vice-President Gore in Florida in 2000.   Gore v. Bush eventually wound up in the Supreme Court, but it first had to work its way through Florida’s state court system.

If we were to have a national popular vote system, this would mean overlying a purely Federal election over 51 state elections.  This isn’t impossible, but it does need to be thought through and carefully implemented.  Polling times, voting procedures, time and manner of ballot counting,  eligibility to vote, probably ballot design,  and so on should be standardized for a Federal election.  For example, in some states convicted felons who have served their sentences can vote, and in others they cannot; in a national election, a uniform standard should be adopted.  Probably the most important thing is to set standards for a recount: under what conditions should one be held,  who is the supervising body, should the recount be held simultaneously, and so on.

The reason recount procedures are important is that recounts are quite likely.  There  have been 16 elections since the end of World War II.    Of these, three (Kennedy-Nixon 1960, Nixon-Humphrey-Wallace 1968, Bush-Gore 2000) have come within the 0.5% threshold at which most states order automatic recounts.  Three more (Truman-Dewey-Thurmond 1948, Carter-Ford 1976, Bush-Kerry 2004) were within a couple of percent and might have been challenged.  Almost one Presidential  election in five results in an automatic recount, and another one in five in a possible recount.

Fair Vote prefers a national popular vote, and discounts the possibility of a national recount.  A Fair Vote conducted study shows that only one election in 332, almost exactly 3 in 1000, gives rise to a recount.  The Fair Vote study is correct but irrelevant.  Most elections in the United States are uncontested, or offer only token opposition to the certain winner.  This is partly due to the sheer number of elections we have in the United States: here, we elect many minor officeholders who are appointed in most countries.  Uncontested elections are partly due to gerrymandering; and partly due to dominant regional party strength.  Such effectively-uncontested elections form the great bulk of the elections in Fair Vote’s study.  However, all Presidential elections are hotly contested in an evenly-divided polity, and in these circumstances extremely close elections are frequent.

Finally, should we insist on a majority, or simply a plurality?  In most of our popular elections, it’s the latter, but there are exceptions.  A number of states (Louisiana, for example) require a runoff between the top two candidates in the event that no candidate wins a majority on election day.   This is also the case in a number of popular-vote countries, notably France.   Whether we should require a majority  is no idle question: in the 16 elections since World War II,  no candidate won a majority in five elections, and  in a sixth a candidate won a majority  by just eight-hundredths of a percent.  We’ve had a majority requirement in the electoral college since the dawn of the Republic; should we carry this forward to a majority requirement in the popular vote.

There’s actually an ingenious proposal to introduce a National Popular Vote without going through a Constitutional Amendment, and it’s getting some traction.  It’s brilliant, but in our opinion fatally flawed.  We’ll look at that one next.

## The National Popular Vote Without An Amendment: A Great Idea that Just Won’t, and Shouldn’t, Fly.

But you just have to love the sheer brilliance of the idea.

The National Popular Vote Bill is the brainchild of Dr. John R. Koza, the founder of Scientific Games, Ltd.  The basic idea is to enlist state legislatures to pass bills which commits those states’ electoral votes to the winner of the national popular vote.  The commitments wouldn’t take effect until states with at least 270 votes passed similar legislation.

The sheer brilliance of the idea is also its most significant, and really only,  flaw:  Dr. Koza and his colleagues have devised a way to effectively amend the Constitution without going through an amendment process.  This leads to a host of problems, which we detail here:

• The first problem is inherent: this is an attempt to end-run a Constitutional Amendment.  It’s a good question as to whether a subterfuge like this is Constitutional; there are two  procedures to amend the Constitution, and one has been used successfully 29 times, so the procedure is not too burdensome.    The second procedure is entirely in the hands of the states.  The National Popular Vote bill invokes neither; instead, any compact of states with 270 electoral votes between them could effectively, by statute, modify out system of government  Any Supreme Court might well hold that the Constitution cannot be amended by as few as 11 states acting on their own (California, Texas, New York, Florida, Pennsylvania, Illinois, Ohio, Michigan, Georgia, New Jersey, and North Carolina).  The National Popular Vote people, counter, correctly, that the Constitution permits each state to select electors by any manner it chooses, so long as all electors are chosen on the same day.  However, it is implicit in the Constitution’s wording that the electors be chosen by the people of the state or by their representatives; it is by no means clear that the legislature of a state can abdicate the choice to the voters across the nation.   Further, Article 1, Section 10, Clause 3 of the Constitution explicitly prohibits states from entering into compacts without the consent of Congress: “No State shall, without the Consent of Congress,…, enter into any Agreement or Compact with another State”.  At a minimum, the National Popular Vote bill is constitutionally dubious, which means it is certain to be challenged in court.  There is a good review of the issues involved here, with a pro-Popular Vote perspective:  The Constitutionality of the National Popular Vote: Refuting Challenges Based on Article II, Section One
• The incentive to cheat in a close election is very large.  Our history has shown that partisans are more than ready to ditch high-minded good-government principle for party advantage on any slight excuse.  So consider the scenario where the 11 states mentioned above have joined the National Popular Vote compact, and no others have.  Now assume a Republican has narrowly won the popular vote, by a tenth of a percent or so, but nine of the 11 mentioned states (every one save Texas and Georgia)  have voted for the Democrat, some convincingly.  Finally assume that the Republican  has won less than 220 of the 269  electoral votes allocated to states which have not, in this scenario, passed the National Popular Vote bill.  The morning after the election the outraged citizens of California,  Pennsylvania, Michigan, New Jersey et al will demand that the legislature recant the National Popular Vote act and select electors in accordance with the wishes of the state’s voters.    The cheerleaders of the partisan media (slate.com, MSNBC, and so on) are sure to find good reasons for their renunciation.  [If this example seems offensive to the Democrats among my readers, simply reverse Democrat and Republican in the above example, choose different states, and insert Fox News and Newsmax.com in the above; it would be no less credible].   The National Popular Vote Compact organization has, of course, considered this and put protections into their bill: a “blackout” period after July 20 in an election year,  prohibiting NPV Compact states from changing their electoral laws after that date.  FairVote also claims that Article I, Section 10, Clause 1 of the Constitution prevents states from refusing to honor interstate compacts.   The cited clause reads: “No State shall enter into any Treaty, Alliance, or Confederation; grant Letters of Marque and Reprisal; coin Money; emit Bills of Credit; make any Thing but gold and silver Coin a Tender in Payment of Debts; pass any Bill of Attainderex post facto Law, or Law impairing the Obligation of Contracts, or grant any Title of Nobility.”.  This doesn’t require states to keep their word to each other, and in any case Clause 3 says that they can’t enter into treaties with each other without getting Congress’ permission.
• The final problem is that the states in the National Popular Vote Compact have no means of enforcing voting standards among the states that join the National Popular Vote Compact, much less the other states.  Under the National Popular Vote Compact, California will be casting its electoral votes for the candidate preferred by all 50 states and the District of Columbia.  But how does California know how those votes were cast?  More importantly, how does California know who won?  Consider, for example, a Kennedy-Nixon election of 1960, where the national popular vote winner (Kennedy) was defeated in California.  Kennedy won the national popular vote by only 16 hundredths of a percent: well within the automatic-recount margin for virtually every state.  Nixon won California by about 54-hundredths of a percent, just barely out of automatic-recount territory.  Question.  Under the National Popular Vote Compact, for whom should California cast its electoral votes?  Kennedy?  But under California law, Nixon could surely demand a recount.  But the recount would have to be national, and how could California coerce a non-compact member (say, Rhode Island) to conduct a recount?  Rhode Island  voted for Kennedy by over 60%, and let’s assume it isn’t a member of the compact; it’s casting its four electoral votes for Kennedy, inarguably, and has no internal reason to go through the expense and trouble of conducting a recount.  But there is no way that any state would accept a 16-hundredths of a percent margin without a recount; what is California to do?

For all of these reasons, whatever one thinks of the idea of a National Popular Vote, the National Popular Vote Compact is both a brilliant and a terrible idea.  In a close election — and the only time any of this really matters is in a close election — the National Popular Vote Compact is certain to cause chaos at a level that would make Bush-Gore 2000 look staid by comparison.  The result would certainly be a repeat of what happened following the tumult of 1800; the National Popular Vote Compact would collapse of its own internal contradictions and failings, much as the original election procedure laid out in Article II, Section 1 of the Constitution collapsed, and a Constitutional Amendment would fix things up, much as the 12th Amendment gave us our current election procedures.

The fact that Congress and the States will eventually be shocked into fixing our broken electoral college system by a disaster caused by the National Popular Vote Compact, though, is no reason to deliberately foster the disaster.

In the next post, we’ll look at adoption strategies for the Threshold Proportional Vote.

## Comparisons to Other Reforms

In previous posts, we introduced the Threshold Proportional Vote and showed how it would work in practice.   In this post, we’ll look at other proposals for electoral college reform.

This isn’t the only proposal for electoral college reform.    There are three  proposals that have received a great deal of attention: a national Maine-Nebraska system,  the Pure Proportional Vote System, and the simple direct popular vote scheme.   The last of these three schemes is a sufficiently interesting and discussed topic that it deserves its own post, and we’ll do that in the next post.  In this post, we will look at the first two proposed reforms: the National Maine-Nebraska System and the Pure Proportional Vote system.

The Constitution allows the states to pick their electors by any method they choose, and states have experimented with a number of methods in the past.  Currently, 48 states and the District of Columbia use the familiar winner-take-all method, but Maine and Nebraska each select two electors statewide and one for each Congressional District.  In 2008, in fact, Senator McCain won Nebraska and two of the CD’s, and President Obama won the district around Omaha: Nebraska split its electors, 4-1 for McCain.

So the National Maine-Nebraska plan is to elect one elector for each of the nation’s 435  CD’s, two from each state, and three from the District of Columbia.  The attractions of this plan are  that candidates would have to campaign not only in battleground states but also in battleground CD’s, and that the Battle of the Chads in Florida would have been only over the two statewide EV’s, not all 25 of Florida’s EV’s.

Attractive.  Unfortunately, an analysis of recent elections shows a couple of things (data from the Swing State Project):

• [Bad] There aren’t all that many competitive CDs.  58 CD’s were decided by 5% or less in 2008; 45 in 2004; 49 in the squeaker of 2000.  Forcing candidates to fight for CD’s really isn’t expanding the electoral map much.
• [Fatal].  The National Maine-Nebraska system shows an overwhelming bias for the GOP.  In 2000, under a National Maine-Nebraska System, Bush comfortably beats Gore, 298-240, despite losing the popular vote.  In 2004, Bush’s 2% popular vote squeaker over Kerry turns into a 90-vote 314-224 margin in the electoral college.  In 2008, Obama’s six-point landslide over McCain yields a 303-235 win.

The latter flaw is fatal: quite aside from the right and wrong of any system with a strong partisan bias, any meaningful reform will require the support of both parties.  In other words, the National Maine-Nebraska System is deader than a doornail.

## The Pure Proportional Vote

The pure proportional vote is a simple system: if a state has n electoral votes,  and a candidate gets p% of the vote, he gets p * n/100 electoral votes.  So, for example, a candidate who gets 43% of the vote in California gets .43 * 55 = 24 electoral votes.  There will obviously be steps due to rounding.  This seems quite similar to the Threshold Popular Vote, and is on the surface quite fair.  FairVote.org endorses it as a reform, which may indicate that FairVote has a strong preference for systems which favor third-party candidates.  However, on the evidence, the voters don’t like it much.

The Pure Proportional Vote has been proposed once before: in Colorado, in 2004, as Amendment 36 to the Colorado Constitution.  It got drubbed in a referendum, 66%-34%.  A defeat this stunning leaves scars, but also teaches lessons, and the lessons are best taught by perusing the arguments of the opponents: Coloradans Against a Really Stupid Idea (CARSI).   Essentially, this group made two core arguments:

1. Amendment 36 gave each candidate the exact proportion of electoral votes corresponding to their popular vote total.  Colorado had nine electoral votes, so this essentially amounted to awarding a candidate one electoral vote for each 11% of the popular vote he got.  The losing candidate in Colorado generally gets about 45% of the popular vote or more, so one electoral vote would be up for grabs in Colorado in every election.
2. The Amendment would have applied to the 2004 election, when Bush was virtually certain to carry Colorado and Kerry to get 45% of the vote or so; since Colorado was the only state adopting this, this amounted to a net win for the Democrats of four electoral votes.  The Amendment was sponsored by Democrats from California, and the Republicans had no difficulty discerning that this was simply a blatant attempt to grab a few extra electoral votes in a tight election.

CARSI’s first objection is essentially that normal variation in popular vote won’t be enough to sway electoral votes; it takes too much change in the percentage of the vote to change any electoral votes.  To avoid this problem, we have advocated a threshold proportional vote system.  Under our system, in a state with nine electoral votes like Colorado, a candidate would get nothing for the first 40% of the vote, and then one electoral vote for each 2.222% of the vote thereafter; in contrast, Amendment 36 would have awarded each candidate one electoral vote for each 11.1111% of the popular vote.  Under the threshold proportional vote  system, every election would have several electoral votes up for grabs from Colorado.

The second objection is serious, and makes the point that the means of introduction of a new system is as important as the new system itself.  In enumerating the requirements for any new electoral system, we observed that any new system must not favor one party over another, nor should it leave any  state materially worse off than it currently is.  This is also true of its means of introduction.   If  all Democratic-leaning states adopted the Threshold Proportional Vote  system, and Republican-leaning states did not, this would lead to a strong bias in favor of the Republicans, and of course the converse is also true.  As a result,  the Threshold Proportional Vote  system must be introduced simultaneously, in a balanced way,  in Republican and Democratic leaning states.  Further,  it must be extremely difficult for states to return to the winner-take-all system, to avoid the problem of last-minute shanges to affect an election.  We’ll note this as a potential problem with the National Popular Vote Compact in the next post.