- ...NP-hard
- A problem is said to be
*NP*-hard if it cannot be solved in polynomial time. If*n*is a variable describing the complexity of the problem (for example, number of voters or number of alternatives), we say that the problem can be solved in polynomial time if we can solve it in*n*, 6#6, 7#7, or another power of*n*steps. On the other hand, if the problem requires 8#8, 9#9, or another number raised to the 10#10 power steps to solve, it becomes quite intractable as*n*increases and is thus*NP*-hard [53]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- ...scale.
- The concept of utilities is theoretically grounded in
the Von Neumann-Morgenstern method of determining cardinal measures
of preference [104] However, in reality many people are
unable to understand this method or use it to determine their
utilities. Less precise estimates of utilities will often suffice.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- ...``chad''
*The New Hacker Hacker's Dictionary*explains a possible origin for the word chad:One correspondent believes

*chad*... derives from the Chadless keypunch (named for its inventor), which cut little u-shaped tabs in the card to make a hole when the tab folded back, rather than punching out a circle/rectangle; it was clear that if the Chadless keypunch didn't make them, then the stuff that other keypunches made had to be `chad' [84].. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- ...cryptography
- Public-key cryptographic algorithms use a pair
of cryptographic keys: a public key and a private key. A message
encrypted with a public key can only be decrypted with the
corresponding private key and
*vice versa.*In addition to protecting secrets, public key cryptography can also serve as a digital signature to authenticate electronic documents.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- ...signatures
- Blind signatures allow a document to be signed
without revealing its contents. The effect is similar to placing a
document and a sheet of carbon paper inside an envelope. If
somebody signs the outside of the envelope, they also sign the
document inside. The signature remains attached to the document,
even when it is removed from the envelope. Chaum [29] and
Schneier [95] provide more background information on
public-key cryptography, digital signatures, and blind signatures.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- ...pamphlet
- Dodgson's unpublished pamphlet
``A method of taking votes on more than two issues,'' is reproduced
as an appendix to [13].
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- ...HREF="node13.html#figblack">.
- Note that the example assumes that
the predicted outcome ranks candidate 1 in first place, 2 in
second place, and 3 in third place. If this predicted ranking
does not match the voter's preference ranking, the appropriate
substitutions must be made. For example, if the voter had the
preference ranking 3 over 2 over 1, the voter's 50#50 would
refer to the probability of a tie between candidates 2 and 3.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

- ...approximation
- Thanks to Professor Edward
Spitznagel for suggesting this approximation.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .