"HOW VOTES are counted, and who counts them, are issues as important as who votes."

That sentiment didn't come from the notoriously corrupt Tammany Hall politician Boss Tweed, who never met a ballot box he couldn't stuff, but from signage at the National Museum of American History, where the exhibition "Vote: The Machinery of Democracy" reminds viewers not once, but on four separate text panels, that it's the counters after all, and not the voters, who determine elections.

As if we needed reminding.

While the show does contain such items as a magnifying glass, used during examination of Florida's infamous "hanging chads" during the 2000 presidential election, "Vote" goes back much further than that, offering up a small but timely and important history lesson on, as the name implies, the machines and apparatus that have been used over the years to record, collect and tabulate our votes. I don't think it's meant to be, but with its replica of a false-bottom ballot box (perfect for slipping extra ballots in while bypassing the lock), sample butterfly ballot (remember that one?) and other unreliable-looking devices from the history of American democracy, this is kind of a scary show.

Scariest of all might be the crazy quilt map printed on the floor of the museum, which shows, by jurisdiction, exactly what parts of the country use what kind of voting machine today. The sheer lack of standardization -- choices include optical scanners, electronic devices, pre-scored punch cards, mechanical levers, paper ballots, computers and some combination of the above -- is enough to give you the willies. Examples of all of those options, including a "Star Trek"-looking IBM Port-A-Punch and stylus from 1959, a precursor to the more familiar Votomatic machine, are included for your perusal.

You'll find another Votomatic, this one from Florida's Miami-Dade County, on view (and for sale) at Banning+Low gallery, a year-old shop on Kensington's Antiques Row specializing in posters, vernacular photography and other ephemera. There, in "William Jennings Bryan-GeorgeWalker Bush: A Century of American Political Memorabilia," a thematic exhibition of buttons, editorial cartoons, bumper stickers, placards, press photos and other detritus of bygone campaigns, you'll also find a mini-retrospective sampling the satirical political art of Washington-based Charlie Mendez.

In Mendez's prime, his witty work could be regularly found in the pages of Washingtonian, Smithsonian, Changing Times and other publications. His 2-D and 3-D work, the latter of which he molds out of something called Durham's Rock Hard Putty into tiny painted busts, might be called a kind of "conceptual caricature," going less for the obvious exaggeration of physical features than for subtle but pointed commentary. To be sure, Mendez has given Bill Clinton's nose a decidedly Nixonian (albeit a bit more phallic) dimension in "Bulletproof." Still, in this sculpture, in which Clinton's visage appears above a Jasper Johns-like target -- ringed by bullet holes against a backdrop of newsprint -- it isn't so much the president's likeness that we laugh at, but its hydralike repetition.

Similarly, Mendez's George W. Bush as a slapstick-wielding "Punch" the puppet is surprisingly kindly rendered, considering the beady-eyed, jug-eared predilections of other artists who have drawn him. Yet it's in Mendez's larger concept of the piece, which I'm told includes a companion John Kerry as a similarly armed "Judy" (sadly not on view here) that the work's message about negative campaigning lies.

Don't get me wrong. Mendez's art can be mean. If anything, the small selection of pieces here seems to have been carefully edited to avoid offending certain customers in heavily Democratic Montgomery County, where frequent Mendez targets Clinton and Jimmy Carter are remembered fondly by many.

John Low and his father, Jack Banning, opened this esoteric gallery and shop last September and have already featured the wry, manipulated street signs of contemporary artist Richard Kelly Tipping. In the future, Low hopes to be able to devote greater space and attention to a wider variety of work by Mendez, and I encourage him in that endeavor.

VOTE: THE MACHINERY OF DEMOCRACY -- Through Jan. 30 at the National Museum of American History, 14th Street and Constitution Avenue NW (Metro: Smithsonian, Federal Triangle). 202-357-2700 (TDD: 202-357-1729). americanhistory.si.edu. Open daily 10 to 5:30. Free.

WILLIAM JENNINGS BRYAN-GEORGE WALKER BUSH: A CENTURY OF AMERICAN POLITICAL MEMORABILIA -- Through Sept. 12 at Banning+Low, 3730 Howard Ave., Kensington. 301-933-0700. www.banningandlow.com. Open Tuesday-Friday and Sundays 10 to 5:30; Saturdays 11 to 6. Free.

Broward County, Fla., canvassing board member Judge Robert Rosenberg examines a disputed ballot in 2000, from "Vote: The Machinery of Democracy" at the National Museum of American History. The Port-A-Punch, invented by Joseph P. Harris, who sold the patent to IBM in 1965. Charlie Mendez often targeted Jimmy Carter, as in the drawing "Carter: Lusting in His Heart (Playboy Interview)."