May 31, 2016

One More PPDI

For a long time, my Web site has contained a list of pluperfect digital invariants (PPDIs) in bases 2 through 10. Recently, I have been finding and posting PPDIs in larger bases. I just revised the list of base-11 PPDIs, fixing minor (mostly formatting) errors and adding an order-9 PPDI that had been omitted, namely,


which is 2,295,894,300 in decimal notation.

My page of PPDIs now lists PPDI in bases 2 through 12. I am certain of the correctness of PPDIs in the first 10 bases, but I still have to recheck the base-12 list to be sure no numbers were omitted.

No doubt, most readers have no idea what this post is about. I have written it just in case it is of interest to someone who finds my blog. In particular, if anyone is relying on my base-11 list, he or she needs to know that the number above is also a PPDI.

May 22, 2016

Stop Donald Trump, Etc.

Readers may notice a few changes in the sidebar at the right. I removed the list of recent posts because the software that generated the titles no longer worked properly. You can always scroll down to see the most recent posts, of course, and you can also access a complete list of posts in the Blog Archive near the bottom of the sidebar. Remember that a similar list, along with information about each post is available in the blog Table of Contents. (See Links at the right.)

I have removed the Christian Diversity badge from the sidebar, not because I believe any less in Christian diversity, but because I needed the space for something more pressing. That more pressing need is to help elect a reasonable President of the United States.

The Republic might not survive a Donald J. Trump presidency. People of good sense and goodwill need to do everything in their power to prevent the catastrophe that would represent. In this spirit, I am displaying the graphic below, which will become a regular part of my blog’s sidebar.

Save the Republic. Stop Donald Trump.

I encourage readers to use this image freely on blogs, on Facebook, and elsewhere on the Web and off.

A design note: The text color in the above graphic was inspired by Mr. Trump’s hair. (Did you catch that?)

May 19, 2016

How We Vote, Part 3: Early Voting

VoteAbsentee ballots have long been available to voters who expect to be out-of-town on election day or for whom, due to disability, find voting at the usual polling place burdensome. In recent years, states have broadened the acceptable justifications for requesting an absentee ballot, so that, in many jurisdictions, if a voter wants an absentee ballot, one will be provided.

A newer idea is early voting, a procedure whereby a person may vote at a polling place some number of days before election day. Like absentee voting, early voting is intended to accommodate those for whom voting on election day is difficult or impossible. By making voting easier to schedule, early voting is intended to increase participation in elections.

Republican legislatures in several states have sought to curtail early voting recently by shortening the period before election day during which votes may be cast. Whatever rationale may have been advanced publicly for such changes, the clear intent has been to make it more difficult for voters thought to favor Democrats to cast ballots.

Liberals have condemned the new abbreviated early voting periods. To be sure, the motivation of Republican legislators has been reprehensible, but early voting deserves more scrutiny than it usually receives.

Early voting does indeed promise greater participation in elections by giving voters more opportunities to fit voting into their busy schedules. This primarily helps blue-collar voters, who are less able to take time off from work to vote than are their white-collar counterparts. It has the added benefit of diminishing waiting lines, particularly on election day. Long lines can cause voters to give up waiting in disgust and simply not voting at all.

Early voting has its drawbacks, however. Too long an early voting period can result in voters choosing candidates based on less information than is available to later-voting citizens. Early voters do not see late-running political ads or endorsements, and they cannot react to late-breaking news about candidates, either positive or negative. A candidate might even be arrested or die between the beginning of the early voting period and election day!

I was made keenly aware of the perils of voting early in the recent Pennsylvania primary. A friend who votes by absentee ballot because of mobility issues voted for one candidate because he was from the Pittsburgh area. (The other candidate considered was from Philadelphia.) Unlike most of her votes, this one was something of a stab in the dark for a lesser publicized office. I voted on election day and was inclined to employ the same logic for selecting a candidate as my friend. Shortly before election day, I learned of “my” candidate’s anti-choice leanings, however, and chose instead to vote for the candidate recommended by Planned Parenthood. My friend was sorry she mailed in her ballot early. (Pennsylvania does not provide for early voting, by the way, and does not allow for “no-excuse” absentee voting.)

There is merit to early voting, and Republican efforts to do away with it should be resisted. But voters can be given flexibility regarding voting dates without creating a lengthy early-voting period. A month or more is simply too long. I see no reason to allow more than a week for early voting, assuming that voters for whom this imposes a hardship can vote by absentee ballot.

Update, 10/1/2016. The presidential election is more than a month away, and several states are already allowing early voting. This is foolish. There are more presidential debates to follow and, no doubt, damaging revelations about one or both of the major candidates.

May 18, 2016

How We Vote, Part 2: Superdelegates

VoteAs the Democratic presidential primaries have progressed, Bernie Sanders has repeatedly complained about superdelegates. These are delegates to the Democratic National Convention who are mostly party leaders and Democratic officeholders. Superdelegates are not bound by the results of party primaries and can vote for whoever they like for their party’s standard bearer. Every Democratic member of Congress, for example, is a superdelegate. The lack of congressional endorsements is therefore of greater concern to Bernie Sanders than it might, at first, appear.

Going into the convention this summer, Hillary Clinton will have won more pledged delegates and received more votes than her opponent. In fact, she will likely have enough votes to win nomination even without the votes of superdelegates. Sanders only hope—a hope that, at this juncture seems completely irrational—is to prevent Clinton from winning an outright victory by virtue of accumulating pledged delegates and to convince virtually all of the superdelegates to vote for him. His quest for the nomination would be easier if there were no superdelegates, since a contested convention would then result if Clinton failed to garner sufficient pledged delegates.

Does the existence of superdelegates make the primary battle unfair? Does it make it undemocratic? I don’t think so. For one thing, superdelegates are inclined to go along with the will of the people, as expressed in the presidential primaries. This is what happened in 2008, when Barack Obama led Hillary Clinton in primary voting, albeit not by much. Perhaps more importantly, superdelegates provide insurance against Democratic voters selecting a candidate thought unelectable by the professional politicians. (Were Donald Trump running as a Democrat, I have no doubt that superdelegates would be voting for someone else.)

This is not to say that professional politicians have a corner on political wisdom, but they are professionals and, at the very least, are likely to have more informed and sophisticated judgement regarding political races.

Are not superdelegates supremely conservative in their effect? Don’t they make political revolutions impossible? Yes, they do, but this is not a bad thing. Bernie Sanders’ call for a revolutionary change in American politics is a naïve dream. The American ship of state does not turn on a dime; change takes time. Trying to change any other way leads to the French Revolution (or, at the very least, the Democratic Nevada Convention).

Despite what Senator Sanders thinks—and his rhetoric gets progressively angrier as has candidacy approaches definitive failure—superdelegates are not a plot to deny him the nomination. Instead, they provide a safety net for the Republic that, in this age of The Donald, looks like a very good thing.

There is no such safety net in November. If Americans elect Donald Trump, the United States will go over the edge, with unpredictable, though certainly terrible results.

May 17, 2016

How We Vote, Part 1: Open Primaries

In the long run-up to the 2016 presidential election, I have frequently found myself thinking about how we vote in this country, in general and in party primaries. I had planned to write one long essay on the subject, but it quickly became clear that such a plan was too ambitious, at least if I wanted to post something anytime soon. Instead, I am beginning a series of more modest posts about voting. I begin with the subject of open primaries, a completely arbitrary starting point. More essays will follow. As always, comments are welcome.

Open Primaries

Bernie Sanders has expressed frustration over how states like New York conduct presidential primaries. In particular, he has complained about the inability of independents to vote in the Democratic primary because he seems to be especially popular with such voters.

In fact, states like New York have it right, insofar as they are discriminating as to who can vote in a Democratic or Republican primary election. The purpose of presidential primaries is to help select the candidate who will best represent a given party in the general election in November.

It makes no sense to allow Democrats to vote for the Republican candidate or Republicans to vote for the Democratic candidate. Allowing such crossover voting invites mischief. A Democrat, for example, could choose to vote in the Republican primary not for the strongest candidate, but for the candidate thought easiest for a Democrat to beat. (I imagined a certain satisfaction I would have felt had I been able to vote in the Pennsylvania primary for Donald Trump, a sociopath supremely unqualified for holding high office.)

Allowing a member of one party to vote in another party’s primary distorts the results in both primaries, as one party obtains an extra vote, and the other party is deprived of a vote. This could have the effect of obscuring the popularity of particular candidates as well as the likely turnout of partisans in the general election.

Why shouldn’t a registered independent be allowed to vote in a Republican or Democratic primary, however? To answer that question, we need to think about what it means to register as an independent. Independents are treated differently in different states.

In New York, for example, a voter can register as a member of one of eight different parties, including the Green party and the Women’s Equality party. One can also specify a party not listed on the registration form. A voter can choose to check the box indicating that “I do not wish to enroll in a political party.” Moreover, New York does not allow a voter to change registration except far in advance of an election. It is clearly a state that doesn’t want voters gaming the system.

New York is unusual in listing so many parties on the voter registration form, but it is common for states to allow a party to be written in or for a voter to indicate allegiance to no party when registering. Most states allow registration changes closer to elections than does New York, the extreme case being implemented in states such as Colorado and Wyoming, which allow same-day registration.

No doubt, New Hampshire is a favorite state of Bernie Sanders. There, one can be unaffiliated and still vote in either the Democratic or Republican presidential primary. By voting in a primary, you are automatically registered in the party for which you cast a vote. Before you leave the polling place, however, you can re-register as an independent.

If you are registered as a minor party member, say the Libertarian party, you should not be allowed to vote in either the Democratic or Republican primary by the same logic advanced above—you should not be able to influence the decision-making of a party not your own.

A true independent (or uncommitted) voter, on the other hand, is one who has chosen not to be associated with any party. Many people, I suspect, eschew registration in a party out of frustration with the major parties (or parties in general) or because they feel a need for selecting candidates solely on their individual merit.

If you are unwilling to be associated with a particular party, however, why should that party allow you to participate in making one of its most important decisions? Senator Sanders would, no doubt, argue that allowing independents to vote in a party primary is helpful in predicting how swing voters will vote in the general election. There are at least two problems with this argument.

First, there is no direct way of knowing how independent voters have voted. Vote tallies do not tell us. Only through exit polling can we distinguish between the behavior of loyalist voters and independents. Like all polling, exit polling is subject to error.

Perhaps more importantly, the independence of uncommitted voters makes it difficult to know how they will vote in November. An independent voter who is allowed to vote for Sanders may well decide to vote for Donal Trump in November if the Democratic nominee is Hillary Clinton. Or the voter, strongly attached to neither major party, may simply stay home.

Thus, arguments for allowing independents to vote in party primaries are weak. Registering as an uncommitted voter in most states means opting out of partisan primaries. That is how it should be.

Postscript. One’s voter registration can be used to send a message. Registered independents are, in some sense, saying “a plague on both your houses.” As a young voter in Louisiana, I registered as a Republican. This meant opting out of choosing most office holders, since, in the time of the Democratic Solid South, election winners were really chosen in the Democratic primaries. My registration was really a vote for competitive elections in my home state. Alas, Louisiana politics are now as bad as ever, but it is the Republicans who are usually in control.

May 10, 2016

Episcopal Journal: We Deserve Answers

I recently wrote about the lack of transparency regarding the firings at the Episcopal Church Center. (See “Thoughts about Presiding Bishop Michael Curry’s Investigation Update.”) Since then, no additional information has been forthcoming from church headquarters.

Episcopal Journal logo
No doubt, many Episcopalians are as frustrated as I about what happened at 815 Second Avenue. (In fact, the operation of the Episcopal Church Center is generally opaque.)

Under the circumstances, I was pleased to read an item (“From the Editor’s Desk”) in the May issue of Episcopal Journal. In it, editor Solange De Santis wrote that “[t]he letter announcing [the personnel actions taken by Presiding Bishop Michael Curry] was as notable for what it did not say as for what it did.” The piece concludes
Why should we have to rely on speculation? Episcopalians support the church’s main office with offerings and prayers. We would like to think that churchwide staff are working efficiently and upholding the principles of the denomination they serve. We deserve more substantive answers.
Perhaps Episcopalians should be emphasizing prayers over offerings.