1 Advances in Political Economy - Department of Political Science

EDITOR’S PROOF

224 G. Serra

323

324

325

326

327

328

329

330

331

332

333

334

335

336

337

338

339

340

341

342

343

344

345

346

347

348

349

350

351

352

353

354

355

356

357

358

359

360

361

362

363

364

365

366

367

368

2.Assessment of the policy platforms: Candidates announce their platformsxL

andxR.

3.The general-election vote: The median voter electsLorR.

Stage 1 does not involve any decision: the candidates are revealed to voters, along

with their valence attributes. The first decision is made in Stage 2 where each candi-

date must announce and promote her platform taking the other candidate’s platform

into account. In Stage 3, once candidates’ skills,vL,vR, and platforms,xL,xR,have

been observed and assessed, the median voter electsLorRto office. All this infor-

mation is common knowledge. The game must be solved by backward induction and

the solution concept is subgame-perfect equilibrium (SPE) in pure strategies. It will

be important to recall that a SPE requires that all strategies form a Nash equilibrium

(NE) in every subgame.

3.5 Results of the General Election

Before stating the main results of this section, some important variables should be

defined. I callvthe difference in skill betweenR’s candidate andL’s candidate. To

be concrete,v≡vR−vL. Note thatvcan take three values:v∈{−V, 0 ,V}.

I callxL∗andxR∗the equilibrium strategies of partiesLandR, andx∗the winning

platform. These parameters will determine the results of the general election, as

indicated in the main theorem on this section. It must be remember that valence was

assumed to be salient enough that|XL|and|XR|are smaller thanV, which implies

that−V<XLandXR<V.

Theorem 1The equilibrium strategies and equilibrium outcomes of this election for

given values ofvL,vR,V,XLandXRare given in Table1,wherev≡vR−vL.

There are several comments to make about Table1.^3 First note the results when

v=0, that is, when there is no skill difference between the candidates. Both par-

Ta b l e 1 Equilibrium outcomes of the general election

Va l u e o fv Equilibrium platforms

xR∗andxL∗

Winning platform

x∗

Winning party

V xR∗=XR XR R

xL∗∈R

0 xR∗= (^00) RorLwith
xL∗= 0 equal probability
−V xR∗∈R XL L
xL∗=XL
(^3) The proofs of all the results come in theAppendix.